According to the best available evidence, the first people in the Americas were Paleoindian peoples - the ancestors of modern Native Americans. There are some fringe theories that say "Paleoamericans" beat the Paleoindians to the Americas and later mingled with them. Who were the Paleoamericans? Well, there are two main variations.

• The Solutreans: According to the Solutrean Hypothesis, people from Ice Age France and Spain crossed the Atlantic along the ice shelf, hunting seals along the way. This hypothesis is based on the superficial similarities between Solutrean spearpoints and Clovis spearpoints, the presence of Haplogroup X2 in North America (which is much more abundant in western Eurasia than eastern Eurasia), and the early evidence of human habitation along eastern sites, which were thought to have been impossible under older ideas of how the Paleoindians settled the Americas via Beringia. This hypothesis falls apart under closer examination though. There are several thousand years between the last Solutreans in Europe and the first Clovis points in the Americas. We now know what pre-Clovis technologies looked like and while they do show trends that lead to Clovis technologies, they don't resemble Solutrean ones any more than any other human technology of the day does. The X2a Haplogroup in the Americas is highly divergent from the X2 Haplogroups in Eurasia and doesn't appear to be closely related to the variants in western Europe. Finally, the old Clovis First model of Paleoindian settlement has broken down and we know that pre-Clovis Paleoindians were in the Americas much earlier than previously though, allowing them time to reach those eastern sites. I go into more detail on the Solutrean hypothesis here.

• The Great(er) Coastal Migration: As far as I know, this one doesn't have a formal name. For convenience, I'll call it the Greater Coastal Migration, since it builds off the widely accepted Great Coastal Migration theory. This idea was proposed by Walter Neves in the late 1990s / early 2000s. The Great Coastal Migration is the initial push of our species out of Africa, along the south coast of Asia and ultimately in to Australia. Neves' hypothesis is that the Great Coastal Migration didn't just reach Australia, it also extended up the east coast of Asia, around Beringia, and down in the Americas. When this gets brought up in popular media, it's often incorrectly portrayed as a trans-Pacific Australia-to-South America route but that's not what Neves is talking about. He used physical data, particularly Paleoindian remains from South America (notably the remains of Luzia Woman) to suggest that the initial population in the Americas was more closely related to those in modern Australia than those in modern Siberia. The reason, he says, that these traits persist longer in South American than North America is because the populations in North America intermingled with later populations coming over from Asia earlier and longer. His methods and conclusions are a bit suspect. Projecting modern physical anthropological categories into the deep past is tricky because further back you go the more similar everyone looks and traits that we now associate with certain populations might not have yet emerged / might not have become exclusive to those group yet. Neves has a few supporters, but his idea never really caught on. It got a bit of a boost recently, when a study found minor but widespread genetic links between Native American populations and those of Australia and Melanesia, but these genetic links are not shared with Polynesians (meaning that its unlikely that they got carried across the Pacific by Polynesian explorers). It's looking like Neves might have been partially right, though the timing of exactly when these genes got into the American gene pool still needs to be resolved. Being generous, the Great Coastal Migration may have kept going up around Asia and into Beringia, but instead of getting to the Americas first, they ended up becoming part of the Beringian population (which we've known for a while was formed by a mix of populations coming from different parts of Asia) before moving into the Americas proper.