We first left Africa 60,000 years ago. There were still ice sheets over Europe and neanderthals 20,000 years ago. We are not hairy. Cold weather is tough for us
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There are sites all over South America, Mexico and even one in California that date back 300,000-190,000 years. Modern Humans date back 300,000 years. Humans waiting 140,000 years to leave Africa is hard to believe, and does not explain who made those sites.
Neanderthals died out in Europe 39,000 years ago, but persisted in the ME until 20,000 years ago. Neanderthals were not hairy either, as far as we know.
Neanderthal sites are below the ice sheets were it was warmer (contrary to TV portrayals). Most likely settlements were along natural harbors, river mouths - now hundreds of feet below ocean level today. There is no telling what it was actually like in those days because so much information is either missing, gone or inaccessible. Fortunately, underwater archeology is gaining credence and funds, so one day we may know much more than we do now - which is mostly speculation, assumptions and consensus thinking, a picture puzzle with most of the pieces missing.
I know of lots of evidence that homo sapiens are 200,000 to 300,000 years old. Other homo species are much older and some higher order ones reached well into Asia and even the south pacific.
I have never heard of homo sapiens being in the Americas earlier than 20,000 years ago. There are some that say they got here 13,000 years ago and others say 15,000.
I agree with everything you say except that there are sites in the Americas built by homo sapiens or homo anythings that are 100,000 years old or older. I have never seen that.
I do agree that there is a lot of guessing going on. And one thing we can be sure of, is that whatever we know today will be wrong in a decade.