I think where the game currently plateaus in progression (For me, around where quartz is initially unlocked and the only reasonable way to mine it is to spam bombs at it) is about the right spot for where prestige should be. The growth was pretty solid up until that point, but Stone and Clay both have softcapped income at this point and Sandstone is manageable but hard to get deep level pushes in. I would offer prestige upon unlocking Quartz and let how big of a wall it is be the nudge for actually doing it. Making Sandstone the point for prestige to unlock would also work, because it also has the feeling of being a stat wall, just not as sharp as Quartz is.
Speaking of unlocking more things as layers do, I was expecting more global upgrades to unlock with Sandstone and Quartz like they did with Clay, but there weren't any. I think setting up the expectation of new layers being the big unlock pushes is a good spot to shoot for, even if you need to actually enable those upgrades to be obtainable via prestige. That seems like a good design space for the "early, big and powerful" prestige unlocks before you have to start settling for more mundane numerical buffs.
Anyway, this is a pretty nice demo! I am definitely interested in going past the current phase of the game as it is now.