There is every reason to believe, that the American continents were not discovered only once by a fairly large migration ove a period of probably a millennium, but again and again, by repeated visits and transplantations, from many sources. These people, like the first colonies of Europeans who arrived on these shores, may have encountered some overwhelming resistance to their presence, and died out, thousands of years before any other migrants arrived.
Could they have been seafaring folk, who somehow traveled here from Western Europe or Africa? There is some possibility that there may have been sufficient shoreline available, in a lowered ocean, for several parties in small boats to have pushed off in fairly short hops across the Atlantic. If I recall correctly, the Mediterranean was once a dry rift valley, and only filled when the sea waters in the Atlantic were high enough to come over the natural dam at Gibraltar. A vast global warming was ostensibly given as the reason for the sea waters rising some hundreds of feet or so. And also explain the fairly widespread legends about a huge flood overwhelming the known world of its day.
"The Day after Tomorrow" was really kind of limited in its scope.
The last time the Mediterranean completely dried out was 5 million years ago. Evidence suggests that it has been severely dessicated at least 40 time since then, the last was during the last Ice Age. Scouring marks on the bottom near Gilbralter suggest a massive inflow (broken dam) at the end of the Ice Age.
Seafarers, perhaps, most likely from northwestern Europe. We know well that there were people living along the coastlines; we have cave paintings of marine animals in France and Spain. And the people could well have built skin boats and "island-hopped" along the shore (now the bottom of the Atlantic continental shelf 200-300 feet below sea level). About 50-60,000 years ago, people crossed at least 90 miles of deep ocean from Sunda (modern-day Indonesia) to get to Sahul (present-day Australia and New Guinea.)
One wonders about the discovery of haplogroup X (a European/Middle Eastern genetic trait, absent in most Siberian populations) in precolumbian Indians, and the similarities between the technology and material culture of Clovis and the Solutrian culture of Atlantic Europe at about this time.
The flood stories do seem to reflect time periods postdating the Ice Age. Some flood stories in SE Asia may reflect what happened to Sunda; the Black Sea flood is probably reflected in Greek myth (the Deukalion legend) and in Sumerian and Semitic legends (Gilgamesh and Noah, respectively). The Black Sea flood occurred several thousand years after the end of the Pleistocene (5600 BC versus 9000 BC) but resulted from rising sea levels after the collapse of the Laurentide Ice Sheet in the North Atlantic. The Black Sea, between the end of the Pleistocene and 5600 BC, had been a lake, and was probably a center for Neolithic communities.
BTW, the Mediterranean originated about 5 million years ago, long before any humans existed.
As for multiple migrations to the Americas, that makes sense, based on the skeletons (Eurasian types at Kennewick and Spirit Cave, Australoids in Brazil at Lapa Vermelha). Genetic evidence is tougher, though.
Impossible! Only Republicans and SUV's cause global warming!
Seriously, there was a vast global warming, over many tens of thousands of years; it was the end of the ice age. Old news.