The Polynesians managed to sail and colonize Hawaii at least as early as 1000, as well as colonizing places like Rapa Nui or New Zealand from a starting point of Fiji (and themselves descended from the Melanesians who started from Indonesia). They also probably managed to make it to South America and back, given their use of the South American sweet potato as a major staple.
Hawaii, it should be noted, is a clear contender for "most remote place on the planet", given the lack of even small islands outside of the Hawaiian island channels for thousands of miles.