Well he doesn't have to collect the stones. It could be that whoever is sponsoring Paleo just makes them and gives him new stones and gadgets to test out every now and then

Really the story could just be about Paleo stopping the monster of the week and figuring out what their plan is

The 4 stones are already in his possession once he becomes a rider. The omni stone is created later on. For the extinction stone, he could recieve it from the Extinct.

We're not going to add any more dinosaurs. He will have six forms and then maybe a stand alone "movie exclusive" form with a new set of four power ups.

how about for how he gets the extinction stone, there's a member of the extinct who sympathizes with humanity, and only wants to live alongside them, but he sacrifices himself and gives his power to Paleo?

I don't think that should be the case at all. Of course Thero and MAYBE Quadro, but at the very least Aerial and Aqua should definitely be procured as time goes on.

I wanted the 4 base forms to be available from the start because they're base forms each with equal power, but different stats. For example, how Ghost has Ore, Musashi, Edison, and Newton.

I think it's fine if he has all 4 at the beginning.

But the difference is that Ghost will have like 10 forms at least by the end of it all, whereas Paleo only has six total. On top of that, each Eyecon doesn't have four unique power-ups a piece. Paleo starting off with four forms right out of the gate is like if Drive started with Speed, Wild, and Technic right at the start. Or if Kuuga discovered Dragon, Pegasus, and Titan at the very beginning.

It just feels rushed and gives the main Rider too many options and too many doo-dads to play with without actually having earned any of them.

Quick little vote then:
Paleo starting off with 4 base ambers - 2
Paleo staring with Thero then obtaining the rest later - 1

I personally don't care. But how about I offer a middle ground?

How about if he receives it from an Extinct that found him as a worthy opponent facing him several times through the story until they have on final duel wherein after Paleo wins said Extinct will give him a map to a graveyard for the Extinct ancestors that he kept in secret where he finds the meteor that killed of the dinosaurs and the Extinct of the past inside a chunk of raw unrefined amber inside a cave which was apparently hidden by said Extinct because it gives too much power to its user which Ray takes home to be turned to a meteorite powered amber stone