Everything suggests this is what happened. Polynesian people had for centuries boats that could make such voyages. It’s possible the original settlers got lucky

Everything suggests this is what happened. Polynesian people had for centuries boats that could make such voyages. It’s possible the original settlers got lucky/unlucky but the technology needed for it existed for them. There’s also plenty of history showing smaller pacific islands that are colonized, so it looks like living of fish and the sea is possible and not a problem. There’s plenty of information about this in Wikipedia. Alternatively, you can watch Moana.