When I toured the Southwest, we visited some "Pueblo" ruins that contained features peculiar to Maya cities, specifically, a court for playing ball games. I suspect aspects of MesoAmerican culture spread throughout the Southwest US. This may have been normal cultural diffusion, not necessarily any kind of population migration. It's not too much of a stretch to speculate they might have made it further.

I've heard that the Pueblo culture the Spaniards encountered in the 1600s was already in an advanced state of decline, that it represented the last remnants of a much more evolved culture of the past. The Chaco Canyon ruins certainly represent a state of social organization much more advanced than anything the Europeans found in present day USA. Modern anthropologists think Chaco was abandoned because a drought made the plateau uninhabitable. The Indians of the Southwest still have legends of the magical and powerful Anasazi, the Old Ones. It's how they explain all those deserted cities.

There were "Indian Mounds" all over the US (they are very common in Florida). And the ones in the American Midwest reveal a high level of social organization. It's hard to believe they could have been erected by hunter-gatherer bands, or even primitive agricultural communities. They seem to show evidence of thousands of workers toiling for decades on these structures.

There were also extensive native trade networks in ancient North America. While working on a golf course construction crew at the University of South Florida near Tampa, we found many projectile points and other artifacts. Most were of the local agatized coral which would have been highly prized for its decorative value (there was an outcropping of the stone nearby). But some were of stone not found in Florida, like obsidian. We even found some Folsom points, which would have been ancient even for the makers of the arrowheads we uncovered.

One of my workmates was an anthropology major, and he speculated that the USF golf course site, located on high ground near the local flint and chalcedony quarries on the edge of the Green Swamp near the Hillsborough River, was a trade center where the prized local points were traded for exotic merchandise from far away.

Ancient America had reached an advanced level of cultural development, which for some reason, had declined considerably by the time the first Europeans came. The cause of that decline must have preceded the Europeans. That is the real mystery.