I think the only way to get rid of "Eurocentrism" is to get rid of "predefined" civs and start with generic ones where unique traits, units and buildings of your civilization are somehow organically picked/developed/unlocked as the game unfolds and you name your adversaries as you meet them...
Could be really immersive if done right. Starting with "USA" in 4000BC is such a horrible immersion-breaker.
Caveman2cosmos does this. There's even a gameoption to unlock leader traits with levels of culture.
(It doesn't seem that way in game creation since it makes you pick a predetermined civ and leader, but the leader doesn't really matter with the gameoption active and the civ only determines which starting culture you get- they go by continent.)