diff --git a/libs/pika/affinity/src/affinity_data.cpp b/libs/pika/affinity/src/affinity_data.cpp
index 148bb265aa..21b6ce9ae2 100644
--- a/libs/pika/affinity/src/affinity_data.cpp
+++ b/libs/pika/affinity/src/affinity_data.cpp
@@ -71,7 +71,7 @@ namespace pika::detail {
 
         init_cached_pu_nums(num_system_pus);
 
-        auto const& topo = threads::detail::create_topology();
+        auto const& topo = threads::detail::get_topology();
 
         if (affinity_description == "none")
         {
diff --git a/libs/pika/affinity/src/parse_affinity_options.cpp b/libs/pika/affinity/src/parse_affinity_options.cpp
index bf784e7f76..3072e73d94 100644
--- a/libs/pika/affinity/src/parse_affinity_options.cpp
+++ b/libs/pika/affinity/src/parse_affinity_options.cpp
@@ -86,7 +86,7 @@ namespace pika::detail {
     {
         if (!use_process_mask) { return true; }
 
-        threads::detail::mask_type proc_mask = t.get_cpubind_mask();
+        threads::detail::mask_type proc_mask = t.get_cpubind_mask_main_thread();
         threads::detail::mask_type pu_mask = t.init_thread_affinity_mask(num_core, num_pu);
 
         return threads::detail::bit_and(proc_mask, pu_mask);
@@ -97,7 +97,7 @@ namespace pika::detail {
     {
         if (use_process_mask)
         {
-            threads::detail::mask_type proc_mask = t.get_cpubind_mask();
+            threads::detail::mask_type proc_mask = t.get_cpubind_mask_main_thread();
             std::size_t num_pus_proc_mask = threads::detail::count(proc_mask);
 
             if (num_threads > num_pus_proc_mask)
@@ -481,9 +481,7 @@ namespace pika::detail {
         parse_mappings(spec, mappings, ec);
         if (ec) return;
 
-        // We need to instantiate a new topology object as the runtime has not
-        // been initialized yet
-        threads::detail::topology& t = threads::detail::create_topology();
+        threads::detail::topology& t = threads::detail::get_topology();
 
         decode_distribution(mappings, t, affinities, used_cores, max_cores, num_threads, num_pus,
             use_process_mask, ec);
diff --git a/libs/pika/command_line_handling/src/command_line_handling.cpp b/libs/pika/command_line_handling/src/command_line_handling.cpp
index 4a8b612fe8..ae51aceb7f 100644
--- a/libs/pika/command_line_handling/src/command_line_handling.cpp
+++ b/libs/pika/command_line_handling/src/command_line_handling.cpp
@@ -195,21 +195,21 @@ namespace pika::detail {
     {
         if (use_process_mask)
         {
-            threads::detail::topology& top = threads::detail::create_topology();
-            return threads::detail::count(top.get_cpubind_mask());
+            threads::detail::topology& top = threads::detail::get_topology();
+            return threads::detail::count(top.get_cpubind_mask_main_thread());
         }
         else { return threads::detail::hardware_concurrency(); }
     }
 
     std::size_t get_number_of_default_cores(bool use_process_mask)
     {
-        threads::detail::topology& top = threads::detail::create_topology();
+        threads::detail::topology& top = threads::detail::get_topology();
 
         std::size_t num_cores = top.get_number_of_cores();
 
         if (use_process_mask)
         {
-            threads::detail::mask_type proc_mask = top.get_cpubind_mask();
+            threads::detail::mask_type proc_mask = top.get_cpubind_mask_main_thread();
             std::size_t num_cores_proc_mask = 0;
 
             for (std::size_t num_core = 0; num_core < num_cores; ++num_core)
diff --git a/libs/pika/resource_partitioner/src/detail_partitioner.cpp b/libs/pika/resource_partitioner/src/detail_partitioner.cpp
index 89fc994fa9..39f233e9b9 100644
--- a/libs/pika/resource_partitioner/src/detail_partitioner.cpp
+++ b/libs/pika/resource_partitioner/src/detail_partitioner.cpp
@@ -182,7 +182,7 @@ namespace pika::resource::detail {
       : rtcfg_()
       , first_core_(std::size_t(-1))
       , mode_(mode_default)
-      , topo_(threads::detail::create_topology())
+      , topo_(threads::detail::get_topology())
       , default_scheduler_mode_(threads::scheduler_mode::default_mode)
     {
         // allow only one partitioner instance
@@ -358,7 +358,8 @@ namespace pika::resource::detail {
 
             std::string process_mask_message = affinity_data_.using_process_mask() ?
                 fmt::format("pika is using a process mask: {}.",
-                    pika::threads::detail::to_string(get_topology().get_cpubind_mask())) :
+                    pika::threads::detail::to_string(
+                        get_topology().get_cpubind_mask_main_thread())) :
                 "pika is not using a process mask.";
             auto omp_proc_bind = std::getenv("OMP_PROC_BIND");
             std::string omp_proc_bind_message = omp_proc_bind ?
diff --git a/libs/pika/runtime/src/runtime.cpp b/libs/pika/runtime/src/runtime.cpp
index 350a90ab98..c8718af5ee 100644
--- a/libs/pika/runtime/src/runtime.cpp
+++ b/libs/pika/runtime/src/runtime.cpp
@@ -998,7 +998,7 @@ namespace pika {
     namespace detail {
         void handle_print_bind(std::size_t num_threads)
         {
-            threads::detail::topology& top = threads::detail::create_topology();
+            threads::detail::topology& top = threads::detail::get_topology();
             auto const& rp = pika::resource::get_partitioner();
             auto const& tm = get_runtime().get_thread_manager();
 
diff --git a/libs/pika/schedulers/include/pika/schedulers/local_priority_queue_scheduler.hpp b/libs/pika/schedulers/include/pika/schedulers/local_priority_queue_scheduler.hpp
index 6d1d074448..096792b43e 100644
--- a/libs/pika/schedulers/include/pika/schedulers/local_priority_queue_scheduler.hpp
+++ b/libs/pika/schedulers/include/pika/schedulers/local_priority_queue_scheduler.hpp
@@ -1084,7 +1084,7 @@ namespace pika::threads::detail {
             queues_[num_thread].data_->on_start_thread(num_thread);
 
             std::size_t num_threads = num_queues_;
-            auto const& topo = ::pika::threads::detail::create_topology();
+            auto const& topo = ::pika::threads::detail::get_topology();
 
             // get NUMA domain masks of all queues...
             std::vector<::pika::threads::detail::mask_type> numa_masks(num_threads);
diff --git a/libs/pika/schedulers/include/pika/schedulers/local_queue_scheduler.hpp b/libs/pika/schedulers/include/pika/schedulers/local_queue_scheduler.hpp
index aefb3cabb0..e468e01c2e 100644
--- a/libs/pika/schedulers/include/pika/schedulers/local_queue_scheduler.hpp
+++ b/libs/pika/schedulers/include/pika/schedulers/local_queue_scheduler.hpp
@@ -98,9 +98,9 @@ namespace pika::threads::detail {
           , steals_in_numa_domain_()
           , steals_outside_numa_domain_()
           , numa_domain_masks_(init.num_queues_,
-                ::pika::threads::detail::create_topology().get_machine_affinity_mask())
+                ::pika::threads::detail::get_topology().get_machine_affinity_mask())
           , outside_numa_domain_masks_(init.num_queues_,
-                ::pika::threads::detail::create_topology().get_machine_affinity_mask())
+                ::pika::threads::detail::get_topology().get_machine_affinity_mask())
         {
             ::pika::threads::detail::resize(
                 steals_in_numa_domain_, threads::detail::hardware_concurrency());
@@ -781,7 +781,7 @@ namespace pika::threads::detail {
 
             queues_[num_thread]->on_start_thread(num_thread);
 
-            auto const& topo = ::pika::threads::detail::create_topology();
+            auto const& topo = ::pika::threads::detail::get_topology();
 
             // pre-calculate certain constants for the given thread number
             std::size_t num_pu = affinity_data_.get_pu_num(num_thread);
diff --git a/libs/pika/schedulers/include/pika/schedulers/shared_priority_queue_scheduler.hpp b/libs/pika/schedulers/include/pika/schedulers/shared_priority_queue_scheduler.hpp
index 0a74c17310..ef41361c65 100644
--- a/libs/pika/schedulers/include/pika/schedulers/shared_priority_queue_scheduler.hpp
+++ b/libs/pika/schedulers/include/pika/schedulers/shared_priority_queue_scheduler.hpp
@@ -903,7 +903,7 @@ namespace pika::threads::detail {
             using namespace pika::debug::detail;
             PIKA_DETAIL_DP(spq_deb<5>, debug(str<>("start_thread"), "local_thread", local_thread));
 
-            auto const& topo = ::pika::threads::detail::create_topology();
+            auto const& topo = ::pika::threads::detail::get_topology();
             // the main initialization can be done by any one thread
             std::unique_lock<Mutex> lock(init_mutex);
             if (!initialized_)
diff --git a/libs/pika/thread_pools/include/pika/thread_pools/scheduled_thread_pool_impl.hpp b/libs/pika/thread_pools/include/pika/thread_pools/scheduled_thread_pool_impl.hpp
index 4be6a57f8e..4aca1229cf 100644
--- a/libs/pika/thread_pools/include/pika/thread_pools/scheduled_thread_pool_impl.hpp
+++ b/libs/pika/thread_pools/include/pika/thread_pools/scheduled_thread_pool_impl.hpp
@@ -283,7 +283,7 @@ namespace pika::threads::detail {
             std::make_shared<pika::concurrency::detail::barrier>(pool_threads + 1);
         try
         {
-            topology const& topo = create_topology();
+            topology const& topo = get_topology();
 
             for (/**/; thread_num != pool_threads; ++thread_num)
             {
@@ -392,7 +392,7 @@ namespace pika::threads::detail {
     pika::threads::detail::scheduled_thread_pool<Scheduler>::thread_func(std::size_t thread_num,
         std::size_t global_thread_num, std::shared_ptr<pika::concurrency::detail::barrier> startup)
     {
-        topology const& topo = create_topology();
+        topology const& topo = get_topology();
 
         // Set the affinity for the current thread.
         threads::detail::mask_cref_type mask = affinity_data_.get_pu_mask(topo, global_thread_num);
diff --git a/libs/pika/threading_base/src/thread_pool_base.cpp b/libs/pika/threading_base/src/thread_pool_base.cpp
index 0a5c6117ef..e6376508f5 100644
--- a/libs/pika/threading_base/src/thread_pool_base.cpp
+++ b/libs/pika/threading_base/src/thread_pool_base.cpp
@@ -38,7 +38,7 @@ namespace pika::threads::detail {
     ///////////////////////////////////////////////////////////////////////////
     mask_type thread_pool_base::get_used_processing_units() const
     {
-        auto const& topo = create_topology();
+        auto const& topo = get_topology();
         auto const sched = get_scheduler();
 
         mask_type used_processing_units = mask_type();
@@ -58,7 +58,7 @@ namespace pika::threads::detail {
 
     hwloc_bitmap_ptr thread_pool_base::get_numa_domain_bitmap() const
     {
-        auto const& topo = create_topology();
+        auto const& topo = get_topology();
         mask_type used_processing_units = get_used_processing_units();
         return topo.cpuset_to_nodeset(used_processing_units);
     }
diff --git a/libs/pika/topology/include/pika/topology/topology.hpp b/libs/pika/topology/include/pika/topology/topology.hpp
index 48526e4152..bd75c4b23e 100644
--- a/libs/pika/topology/include/pika/topology/topology.hpp
+++ b/libs/pika/topology/include/pika/topology/topology.hpp
@@ -244,6 +244,7 @@ namespace pika::threads::detail {
         std::size_t get_pu_number(
             std::size_t num_core, std::size_t num_pu, error_code& ec = throws) const;
 
+        mask_type get_cpubind_mask_main_thread(error_code& ec = throws) const;
         mask_type get_cpubind_mask(error_code& ec = throws) const;
         mask_type get_cpubind_mask(std::thread& handle, error_code& ec = throws) const;
 
@@ -361,12 +362,13 @@ namespace pika::threads::detail {
         std::vector<mask_type> numa_node_affinity_masks_;
         std::vector<mask_type> core_affinity_masks_;
         std::vector<mask_type> thread_affinity_masks_;
+        mask_type main_thread_affinity_mask_;
     };
 
 #include <pika/config/warnings_suffix.hpp>
 
     ///////////////////////////////////////////////////////////////////////////
-    PIKA_EXPORT topology& create_topology();
+    PIKA_EXPORT topology& get_topology();
 
     [[nodiscard]] PIKA_EXPORT unsigned int hardware_concurrency() noexcept;
 
diff --git a/libs/pika/topology/src/topology.cpp b/libs/pika/topology/src/topology.cpp
index 208d5fb8f0..32fcab126a 100644
--- a/libs/pika/topology/src/topology.cpp
+++ b/libs/pika/topology/src/topology.cpp
@@ -52,12 +52,6 @@
 #endif
 
 namespace pika::threads::detail {
-    std::size_t hwloc_hardware_concurrency()
-    {
-        threads::detail::topology& top = threads::detail::create_topology();
-        return top.get_number_of_pus();
-    }
-
     void write_to_log(char const* valuename, std::size_t value)
     {
         LTM_(debug).format("topology: {}: {}", valuename, value);    //-V128
@@ -183,6 +177,23 @@ namespace pika::threads::detail {
     }
 
     ///////////////////////////////////////////////////////////////////////////
+    // We use a function-local static for the topology object so that we don't depend on
+    // initialization order between TUs happening in a particular order and we guarantee that the
+    // object has been created before access. However, we also want to initialize the topology
+    // object early so that we can read the CPU mask of the main thread in case OpenMP wants to
+    // reset it, so we also have a global object call get_topology so that we don't depend on others
+    // calling get_topology early for us.
+    topology& get_topology()
+    {
+        static topology topo;
+        return topo;
+    }
+
+    static struct init_topology_t
+    {
+        init_topology_t() { get_topology(); }
+    } init_topology{};
+
 #if !defined(PIKA_HAVE_MAX_CPU_COUNT)
     mask_type topology::empty_mask = mask_type(hardware_concurrency());
 #else
@@ -193,6 +204,7 @@ namespace pika::threads::detail {
       : topo(nullptr)
       , use_pus_as_cores_(false)
       , machine_affinity_mask_(0)
+      , main_thread_affinity_mask_(0)
     {    // {{{
         int err = hwloc_topology_init(&topo);
         if (err != 0)
@@ -287,6 +299,10 @@ namespace pika::threads::detail {
         {
             thread_affinity_masks_.push_back(init_thread_affinity_mask(i));
         }
+
+        // We assume here that the topology object is created in a global constructor on the main
+        // thread (get_cpubind_mask returns the mask of the current thread).
+        main_thread_affinity_mask_ = get_cpubind_mask();
     }    // }}}
 
     void topology::write_to_log() const
@@ -1119,6 +1135,11 @@ namespace pika::threads::detail {
     std::size_t topology::get_number_of_pus() const { return num_of_pus_; }
 
     ///////////////////////////////////////////////////////////////////////////
+    mask_type topology::get_cpubind_mask_main_thread(error_code&) const
+    {
+        return main_thread_affinity_mask_;
+    }
+
     mask_type topology::get_cpubind_mask(error_code& ec) const
     {
         hwloc_cpuset_t cpuset = hwloc_bitmap_alloc();
@@ -1421,32 +1442,13 @@ namespace pika::threads::detail {
         //print_vector(os, pu_numbers_);
     }
 
-    ///////////////////////////////////////////////////////////////////////////
-    topology& create_topology()
-    {
-        static topology topo;
-        return topo;
-    }
-
-    ///////////////////////////////////////////////////////////////////////////
-    struct hw_concurrency
+    unsigned int hardware_concurrency() noexcept
     {
-        hw_concurrency() noexcept
 #if defined(__ANDROID__) && defined(ANDROID)
-          : num_of_cores_(::android_getCpuCount())
+        static auto concurrency = ::android_getCpuCount();
 #else
-          : num_of_cores_(hwloc_hardware_concurrency())
+        static auto concurrency = get_topology().get_number_of_pus();
 #endif
-        {
-            if (num_of_cores_ == 0) num_of_cores_ = 1;
-        }
-
-        std::size_t num_of_cores_;
-    };
-
-    unsigned int hardware_concurrency() noexcept
-    {
-        static detail::hw_concurrency hwc;
-        return static_cast<unsigned int>(hwc.num_of_cores_);
+        return static_cast<unsigned int>(concurrency);
     }
 }    // namespace pika::threads::detail