There is no evidence at all Neanderthals ever lived in the Americas. Humans did though, and they came much earlier than most people think.
One Pre-Clovis site is Monte Verde:
Monte Verde - Wikipedia, the free encyclopedia
It only dates back to about 15,500 years ago. The best evidence indicates it was settled by Polynesians who had made the Pacific crossing. In addition they found seaweed and all kinds of other interesting stuff there...
There are more Polynesian human bones that were found on Mocha, an Island just off the coast of Chile. There are at least three other sites as well, that I know of.
One of the problems to date with finding such early settlement sites is that prior to about 11,000 BC, the world was very much in an Ice Age. The sea levels were much lower. How much? during most of the Ice age, up to 394 feet lower. This put the original coastline about (and sometimes beyond) where the continental shelf is now. In some places the coast was 100 or more miles from where it is today.
All of the early Coastal settlements, as well as settlements along the coastal river valleys would be undersea archaeological sites now.
In addition, around 12,900 BC North America suffered from a massive meteorite strike that significantly altered the landscape.
12,900 BC - a rain of fire and rock blankets all of North America as a ginormous meteorite explodes then impacts showering unfathomable amounts of rock, ice and earth everywhere killing everything within about a five hundred mile radius, and starting fires which burned everything in Canada East of the Rockies, most of the Western U.S., and the entire central and eastern portions of the United States. Anything that survived the falling debris (including humans) probably starved in the years following the strike as most of the herd animals died as well from lack of edible vegetation...
Exploding Asteroid Theory Strengthened By New Evidence Located In Ohio, Indiana
...and
Six North American Sites Hold 12,900-year-old Nanodiamond-rich Soil
The Impact occurred in Canada just west of the Great Lakes, It's easy to find splatter patterns from the event in Google Maps by looking at Cape Fear, North Carolina using satellite view. You can find the splatter patterns all along the Eastern Seaboard from New Jersey, all the way down to Georgia, and Northern Florida.
...Additional findings:
Impact ~ NEO; Near Earth Objects - Page 5 - Armchair General and HistoryNet >> The Best Forums in History
...and (from 35 years ago)
A RE-EVALUATION OF THE EXTRATERRESTRIAL ORIGIN OF THE CAROLINA BAYS
George Howard's website on the Clovis mini-extinction event and the Carolina Bay formations:
C. Vance Haynes Continental Black Mat in photos
National Academy of the Sciences Website showing the same burn layer
from that single strike in ...Arizona!
Supporting Information
The Cosmic Tusk - Website for the Younger Dryas extinction events
The Cosmic Tusk
At the time, for the peoples living in North America, it was the Apocalypse. It's also why we have so few records of early North American cultures. We don't have these record because the culture that was there, was abruptly wiped out, and never even had the chance to properly create the coprolites and hunting tools, and villages, and campsites, and stuff we find today and call evidence.
Sekhmet thinks the Native Americans are stupid. I just think they were unlucky. If their early civilization had had the opportunity to evolve without interruption, it's very likely the New World explorers from Europe would have met a completely different, much more advanced culture.
