I understand if this is just a headcannon, but I've always assumed that the world from SU is our Earth but set 6000 years in the future, placing the Gem colonisation of Earth in our current day, with Garnet's fusion happening in 250 years, and then the end of the war occouring in about 700 or so years. The weird state of the continents and the countries around the world I always blamed on the Gems terraforming the planet with Gems like Lapis Lazuli, or perhaps attacking the Earth to subjugate humanity (the Tunguska Sea in Russia definitely looks like some kind of orbital attack), and when the war ended, humans could pull themselves together again and try to regain a foothold on their own world over the coming 5000 years, which would explain why the humans of SU have such a different religious, political, and cultural world around them. The New World got rediscovered it seemed, Dewey's ancestor even dubbing Beach City to be a country (which probably joined up with different states like Delmarva and Keystone later on).
In the recent episode "Can't Go Back", Blue Diamond is scolding Pink for always having an excuse not to work on the colony, one of them being "their cities were too hard to dismantle", which to me proves that either humanity was just more advanced back then than humans were in our timeline, or that the humans back then were humans from our present day, our cities would be harder to dismantle than the cities of 4000 BC in my opinion (though of course perhaps this was an excuse and Pink just didnt want to dismantle them).
In short, whilst the AU explanation the crewniverse have told us could be true, I believe it will be revealed to us that SU takes place in the 8000's AD, with the 2000's being when the Gems invade, and that like with other aspects of the show (about a certain character from the recent episodes for instance) they will skew the truth in Q&A's to surprise us with a reveal later on.
Its like you said; the crewniverse has said that the SU universe is an alternate reality. Why would anyone need to 'rediscover' North and South America if everyone already knew they existed? The gem colonization couldn't have taken the generations it would need for nobody to know about the Americas afterwards.
maybe it's set in an alternate earth AND the future. I've wondered whether even though it looks present day perhaps the gems didn't come 6 thousand years from the present but a later time and the reason it looks present is because their invasion stunted humanity's advancement. I remember Pearl learning about knighthood during the war, but knighthood as we know it didn't exist until less than a thousand years ago. and that line about the human cities when urban were only found in the middle east about six thousand years ago is also suspect.
Of course it could just be the writers aren't bearing in mind real history. Then again I considered the possibility that the conflicting information as to where Rose was from was a continuity error, and look how that turned out!