The distance between New Zealand and Tahiti (the approximate origin of the founding population of NZ) is around 2600 miles, longer than the minimum distance between Africa and South America.

You’re not wrong about island hopping but the last hops in the Polynesian expansion - Hawai’i, Rapa Nui (Easter Island), and New Zealand were incredibly remote.

The longest distance between islands is longer than the shortest distance between Africa and South America. So it’s at least possible with relatively primitive technology.

Polynesians had and still have extremely sophisticated stellar and solar navigation techniques (as well as deep observational knowledge of oceans and marine life) that far exceeded recorded European techniques until the advent of tools like astrolabes and sextants in the 1700s, as far as the extent of travel distances. There has been growing evidence of Polynesian contact with South America, including the presence of sweet potatoes (South American origin) which may have just dispersed somehow westward over the Pacific as seeds. But chicken bones (a South Asian origin) have been radio carbon dated to the 1300s in Chile. And a Polynesian settlement in the Auckland islands in the sub-antarctic dating to the 13th century has been found.