What if there had been a fairly extended interglacial starting around say fifty thousand years ago and lasting about ten thousand years?  Make it a somewhat warmer one than the one we are currently in (some of them were considerably warmer than our current temperature).  That gives us a ten thousand year window when voyages along the coast of Asia and then across to the Americas are reasonably feasible.  There wouldn’t be land bridge, but at this point people were capable of getting across substantial bodies of water, as evidenced by the aborigines of Australia.  Let’s say that some body of coastal people from Asia reach the New World during that interglacial.  The ice age resumes around 40,000 year BP and suddenly it gets much more difficult, though possibly not completely impossible to get to the New World.  The fact that the New World is already inhabited makes it harder for any coastwise voyagers that do make it past the ice to actually survive.

You end up with a very isolated population in the New World, probably of people resembling either the Australian aborigines or the Ainu of northern Japan.  That near isolation persists until the next interglacial, presumably starting around ten thousand years ago.  So you have a human population in the Americas, quite possibly coming from a small founder population, with little or no genetic input from the rest of humanity for thirty thousand years.

You also end up with human populations on the periphery of Asia and Europe being more isolated during the early interglacial than they were historically.  The Indonesian islands would all have been islands for the length of that early interglacial—ten thousand years, instead of being connected to the mainland.  Human populations would have diverged on those islands to some extent, both culturally and genetically.  Of course that ends on most of the islands once the interglacial ends.

For the islands like Sulawesa and Timor that don’t connect to the mainland during ice ages, any humans on those islands will have been more isolated than they were historically, and any genetic and cultural differences that develop have a chance to persist during the ice age.

Australia and New Guinea would be even more isolated than they were historically during the interglacial because the higher sea levels increase the ocean gaps between them and Asia.  Natives of New Guinea and Australia, as well as several nearby islands would also be isolated from one another by the higher sea levels, which would make for some interesting interactions when the sea levels go back to ice age conditions.

 Would bringing humans to the New World earlier and not during an ice age mean that some New World animals that historically died out would survive?  How would the natives of the New World develop during their isolation?  What would happen to them when that isolation ended around ten thousand years ago?

What impact would all of this have on humans in Europe?  Would our ancestors invade Europe ten thousand years early during the interglacial?  Or did they lack the technological superiority that they would need to invade Neanderthal territory?  If true humans didn’t invade Europe, would Neanderthal populations grow in the warmer climate?  Would they have more or less contact with our branch of humanity?

Of course all of this assumes an interglacial where current theories say there shouldn’t be one, so that could be a problem.  On the other hand, weather is about as chaotic a system as you can get, so I think I can sort of get away with a little hand-waving here.