It seems that the Clovis first hypothesis has been disproven, and that the Americas were populated at least 20k+ years ago, far before their was an ice sheet on the bearing strait. What are the current theories on the first migrations to America today ?

by rawndale

I quote:

The results of a multiple-author study by Danish, Canadian, and American scientists published in Nature in February 2016 revealed that "the first Americans, whether Clovis or earlier groups in unglaciated North America before 12.6 cal. kyr BP", are "unlikely" to "have travelled to North America from Siberia via the Bering land bridge[52] "via a corridor that opened up between the melting ice sheets in what is now Alberta and B.C. about 13,000 years ago" as many anthropologists have argued for decades.[53] The lead author, Mikkel Pedersen – a PhD student from University of Copenhagen – explained, "The ice-free corridor was long considered the principal entry route for the first Americans ... Our results reveal that it simply opened up too late for that to have been possible."[53] The scientists argued that by 10,000 years ago, the ice-free corridor in what is now Alberta and B.C "was gradually taken over by a boreal forest dominated by spruce and pine trees" and that "Clovis people likely came from the south, not the north, perhaps following wild animals such as bison."[52][53]

If they didn’t come from Siberia over the bearing strait, how did they migrate to here

Reedstilt

The earliest people in the Americas were likely coastal peoples moving along the northern rim of the Pacific from Siberia into the Alaska. Once in North America, these peoples would have continued moving south along the coast, establishing various communities along the way. As these various coastal communities grew, they'd spread out further. Some would head further south along the coast; others would head inland.

By 16,000 years ago at least (possibly as early as 19,000 years ago), people had reached the Appalachians. This is the start of nearly continuous, periodic habitation of the Meadowcroft Rockshelter in western Pennsylvania. This site is particularly interesting with regards to the Clovis question because the roof of the rock shelter partially collapsed during the Clovis period, making it in accessible during that time and sealing the pre-Clovis artifacts off from possible later contamination. This allowed Meadowcroft to be recognized as one of the first definitively pre-Clovis archaeological sites.

Those who headed south reached southern Chile by at least 14,500 years ago, possibly as early as 18,000 years ago. This is when people started inhabiting the Monte Verde site. Monte Verde has the distinction of being the site that put the last conclusive nail in the Clovis-First coffin. The site not only predates the Clovis period by 1500 years, at least, its far removed from the ice-free corridor, necessitating an entirely different mode of migration to reach.

The description you quoted mentioned that "Clovis people" came from the south, not north. While I take issue with referring the Clovis as "a people," the idea of a northward migration fits with the evidence we currently have. This map shows the distribution of Clovis and Clovis-derived points. They're most commonly found in eastern North America, with regions of significant abundance on both sides of the Appalachians. The style appears to have originated in this region and spread out from there.

The reason I hesitate to refer to a "Clovis people" is that the speed at which the Clovis point spreads is more indicative of different communities adopting a new technology from one another, rather than a singular community growing and supplanting others. "Clovis points" were essentially a fad that flourished for about 500 years as the Ice Age drew to a close. It facilitated big game hunting of Ice Age megafauna, but once those animals were out of the picture, people stopped using Clovis points.