True, we haven't found any fossils, but that doesn't mean the process started here. The Gigantopithecus existed in China for around 300K years, then died out apparently. Bigfoots might have evolved in Asia and migrated here in largely their current form. That would explain the lack of finding Neanderthals on North America, and if we conjecture a bit further then the reason we don't see any Bigfoots in the fossil record could be that they haven't been here long enough to be there. A species that potentially is only 15k years old in still in it's primordial infancy.
One day they could be the dominate species on the planet.
And yes, I am simply thinking out loud and typing it out to see what everyone else thinks about it as well. That is what this is all about after all, exchange of thoughts and ideas, even highly hypothetical ones.
How would Gigantopithecus extinction 300,000 years ago explain the lack of Neanderthal remains in America? The former was an ape, the latter a species of human that itself went extinct c.39,000 BP. Besides, at some point Bigfoot would have had to leave remains somewhere. Yet no one has ever found any.