“Men Out of Asia” by Gladwin speculated, back in the 40s, that Central and South America were reached by people out of the Pacific (and he even tought that remnants of Alexander the Great’s fleet were among them). Fascinating (albeit highly speculative) book. It makes sense to me that if Polynesians (and Melanesians?) could populate tiny islands far out in the Pacific, then some number of them would have made it all the way to the Americas.
Thanks Stingray51 for the name of that book and author.