discovery of stone boats
From the Wikipedia section on geology: (emphasis mine)
[A]ll of the great images of Easter Island are carved from the light and porous tuff from Rano Raraku. … The Puna Pau crater contains an extremely porous pumice, from which was carved the Pukao "hats".
Presumably hats were not invented for the statues — people made regular hats for themselves, perhaps as sunshades. They will have noticed that an upside-down hat is like a bowl, our genius realizes the similarity in a concave shape with the dugout canoe.
They would also know, from living there and having lots of rock fragments from the quary industry, that some kinds of rock floats.
So, the stone hat becomes a prototype for a stone boat. The rock is not “closed cell” foam and becomes waterlogged after a while. So they would need to coat the surface or make a skin boat over a stone frame. The latter proves fruitful as they no longer need a solid bowl but meerly a frame.
The return of deep-sea fishing brings the resource of animal skins that they use in more advanced designs. Early fat/mud coatings helped them bootstrap the industry, at least supplimenting the remaining wood boats and taking on seconary roles thus freeing the old boats for deep hunting.
There is no reef system, so not much life in the shallows. They did have some shellfish though.
Why not farm the sedentary shellfish? Modern farmers use dangling lines from a floating platform. If they figured out something like this, they could position them for prime feeding, move them in during bad weather, keep other animqls from preying on them … in fact, attracting other wildlife will become another resource rather than a pest! They are in fact starting an artificial reef! The open fields of shells are bait for the fisherman.
leads to calcium
Now this influx of shellfish has a second effect: shells. There’s no limestone or coral on the island, but shells can serve as the basis for making quicklime.
Having this cement will be useful in their technology and industry. But, it’s not waterproof. The Romans made concrete by discovering volcanic minerals including fly-ash. This is a volcanic island… without digging into the actual composition myself, let’s presume they could find something that, ground up and mixed with the shell, produced a somewhat-useful water-resistent cement upon cooking.
leads to iron?
The idea of cooking rocks leads to the discovery that their island is a rich source of iron ore.
The problem is, they need energy. Without coal, and without trees to make charcoal, their knowledge will exceed their industry at this point.
The nearby islets covered with birds and lush growth — unlike their ruined land — might lead them to discover guano as a source of nitrogen fertilizer. The idea of farming is already established, so they encourage the plants they want, tending them and getting yields greater than the wild.
By this point, they know they want resources for other technological uses, rather than just direct personal consumption. So they grow crops for feeding animals, for use as fuel and building material, etc.