It is quite feasible that the occasional lucky sailor made it across the ocean to the Americas during pre-Columbian times. Maybe even a few fishermen in a boat as long as they didn't eat each other along the way.

Establishing a lasting presence in a new land requires reproduction, or your fortunate landfall is nothing more than the beginning of an extinction event. John Moore, Sociology PhD at the University of Florida, studied the problem and believes the number of breeding couples required to successfully populate a new continent is circa 20 or so.