An "American" civ in 4000 BC clearly isn't historical, but (IMHO) isn't impossible or illogical, either.
I think of the first game as basically happening in a divergent universe (timeline splitting in 4000 BC), on an alternate Earth where the continents are configured differently. (Unless playing on an Earth map).
So, the Atlantic could have been super narrow or non-existent, and the Angles, Saxons and Jutes could have just gone straight to North America (skipping Britain) and migrating much earlier than they did.
On the flip side - why couldn't Romans survive to launch rockets to space? There were an "India" and a "China" contemporary to Rome, end they did end up launching rockets to space. Obviously, it would be a much different "modern day Rome" with likely no columnated porticos etc and legionnaires in sandals, but you get my drift.
It is alternate history but nothing causes cognitive dissonance.
Compare that to Civ VII (I am on my second playthrough now), in both games I don't know who the hell I am playing against and which leader leads which civilization. The game doesn't make this very prominent anyway, I have to hover over banners in the upper right corner to remind myself who is who.
My first game had Jose Rizal, I think, leading, if I remember correctly, Hawaii, then Majapahit, and finally Japan; places thousands of miles away from each other in RL Earth and not very much culturally connected, either.
My current game has Ben Franklin leading Ming, and Lafayette leading the Normans. These can very well evolve into Qing and the Americans, and then when Ben Franklin pops up on the screen, I will always initially presume I'm talking to the Americans.
Huge cognitive dissonance.
(On a separate point - I wish they simply took this opportunity to get rid of immortal leaders. I think the first game had them as a joke; Sid liked humor in his games, and it was funny to see Lincoln in Stone Age clothes and Caesar in a suit I guess. But the current Civs are dead serious and they still have immortal leaders).
Anyway, they made the game the way they did, and I accept that. My only wish is that when there are sufficient numbers of civs and leaders, an option will be added to only allow historical transitions. This won't take anything away from the players who like this approach, but it will mean a lot to players like me.