So over 2000 years, they somehow managed to cross 2/3 of the massive Pacific Ocean in small wooden boats while traveling against ocean currents and using nothing but the stars for navigation. By the 11th century they had made it as far east as Hawaii, the Marquesas Islands and even Easter Island which is only 2300 miles from South America. That might sound like a really long distance, and it is. However, that’s exactly how far they had to travel to get to Hawaii from the Marquesas Islands. So why would they stop at Easter Island or Hawaii, why wouldn’t they just keep on going? Is there any evidence that they made it to South America or even California?
While there may be more to be said, you'll be interested in these responses from /u/reedstilt and /u/cozijo and this response from /u/b1uepenguin.
In short, there are several lines of evidence for which Polynesian arrival in the Americas is a parsimonious explanation. This recent article added some additional support. There is no evidence, however, for the actual contact event: neither region's material culture has been found across the ocean.