Ooooh, strap yourself in for an excellent ride - Polynesian methods of navigation are one of the most awesome things I've run across my time in this sub. Which is not to discourage anyone else; if you'd like to write about how New Zealand or Hawaii were found, please don't let this linkdrop stop you! More answers are forever welcome. While we wait for new stuff, OP, I commend to your attention these previous posts:

• The Oceania section of the FAQ has a good bit of material (the Pacific Islands subsection, if that doesn't automatically take you there);
• and u/b1uepenguin has another answer focusing on both supply and exploration methods - it definitely isn't just "sending boats in arbitrary directions, most perishing without a trace but a few getting lucky";
• and for NZ/Aotearoa specifically, u/LordHussyPants has a relevant post.

As humans spread across polynesia, there always WERE more and more islands without fail, so it's possible it just became an assumption without evidence...that there always would be more islands if you sailed over the horizon. So "whether more islands exist" could just have been an article of faith.

But the direction to sail? That's a trickier one. It could well have been random, similar to the way non-human life can spread out. Or did they have some technology or knowledge that indicated, it's definitely this way. No, not THAT way. Trust me, this way.

For islands in close proximity (as in much of polynesia) it's easy to believe so. But islands THAT far away? Hence my specifying Hawaii or NZ