A game where you start with exactly one animal. You get to choose the type at the start, as each type has slightly different properties and gameplay. You could be a bunny, a cat, a bee, a fox, whatever in a random environment.
Now your goal is to grow your population. Keep finding food, keep getting kids, keep defending against threats, until your population has reached X size and you’ve beaten this environment.
In a sense, this is just the “big number go up”-genre distilled to its essence and given an intuitive (and hopefully cute/cozy) animal theme.
Similar Idea: An infinitely upscaling kingdom builder or city builder (like that Hexagod game I saw). Every time you only work on one section, then once you call it “DONE”, it will keep doing what it does forever and you move to a new one.