The easiest way to do this is by creating a custom map / scenario. Build a ton of archers and 1 enemy villager.
Then go into players select the civilization you want to cross off and then Test the scenario. Your archers will kill the villager and you'll win the match.
Including loading times this takes about 15 seconds per civ. The previously selected Civ will remain selected and be in a red font.
I also tried converting monks and collecting 20 sheep in the Dark Age but to no avail. I think the Civ wins are just unlocked by ANY gamemode