So, it's decades ago that Thor Heyerdahl came up with his theory that Native Americans of the Pacific coast had the boating technology and skill to reach Polynesia. He even built a replica boat (in this case, a balsawood raft, the Kon Tiki) and sailed it from Peru to Tahiti, as a feasibility test. His work was widely popular but dismissed as pseudoscience; I've always considered him one of the great champions undermining what Lewis and Barfield came to call 'chronological snobbery'.
Now some new research in the form of genetic testing suggests that there was contact, but how much is unclear. The Polynesians certainly had the technology to sail just about anywhere in the Pacific
--cf THE PREHISTORIC EXPLORATION AND COLONISATION OF THE PACIFIC by Geoffrey Irwin (1992; highly recommended)--
while for the Americas' side of the story, about which I know far less, certainly the Makah and other whale-hunters of the Pacific Northwest had command of large, powerful boats
-- I have Heyerdahl's massive tome AMERICAN INDIANS IN THE PACIFIC (1953) but have not read it.
In any case, somebody took the sweet potato from South America to spread it across the Pacific, which is pretty good proof of more than casual contact.
Here's the link to the recent article.
Tolkien trivia fact: Tolkien's secretary, Joy Hill, was a friend of Heyerdahl's and had a model of one of his boats he'd given her (I forget whether it was the Tigris or the Ra) on her mantlepiece
P.S.: While we're on the theme of conventional wisdoms showing a few cracks, the late date (12,000 to 14,000 yrs ago) for humans arriving in the Western Hemisphere becomes more Ptolemaic all the time:
alternative universe VI
1 day ago