Some 120,000 years BP, a small group of Homo erectus crossed the Bering land bridge to the Americas. This group would had died *here* without any interaction with H. sapiens, so they did have very little impact in how modern humans evolved and settled the Old World.
The group, however, survived and settled the Americas, evolving into what we will call H. americanus. The americanus settled both North and South America forming small family groups. Hunter-gatherers, they pressured the wild life in the Americas provoking the earlier extinction of a couple of America's megafauna species; but also provoked the evolution of some megafauna species into animals more aware and fear of human presence.
First modern humans
Probably between 40,000 and 25,000 BP, the first modern human beings arrived to the Americas via sea to South America, let's call them Murrayians. Modern human settlements begun displacing americanus, mainly out-competed by the newcomers. Only in the most remote forests and mountains in South America did a few americanus varieties survive in South America, until the next big migration.
Second modern humans
Between 12,000 BP and 10,000 BP, a group of H. sapiens crossed the Bering landbridge into the Americas, let's call them Amurians. More aggressive predators than the H. americanus (or even the Murrayans), together with the climate changes at the end of the glacial era, the Amurians colonization of North America was followed by the virtual extinction of the North American americanus and several megafauna species.