Age of empires 4 doesn't have a random button. This command line tool draws a random civ from the list for you.
If you don't want to pick from all the civilizations you can exclude some using the --exclude flag, passing the first letters of the civs you don't want. You can also select the ones you do want using --include.
- automatically update list of civilizations in case more are added
- make available as a web app