life does actually auto balance, even in humans. Ever noticed countries with higher child mortality rates having higher birth rates too? Other animals have similar behaviours
Exactly. Even if we discovered lightspeed travel tomorrow, journeyed out as far as we could possibly go (i.e. the edge of our local supercluster of galaxies), there would still only be a finite amount of resources available.
Even if those resources would be functionally infinite over a single human lifetime, you'd find on the scale of the universe, they're very much not.
The only thing that might even grow infinitely is the universe itself, and even that we're not sure of.
Because that's not exactly how it works. Nature is finite not because it doesn't try to grow limitlessly, it's that nature grows in equilibrium with the resources and space available in the system/environment.
That often results in the same thing, but the distinction is very important, as if tomorrow there suddenly were infinite resources and space, nature wouldn't just sit there and go "nah, I don't do infinite growth", it would quickly adapt to just grow endlessly.
On a smaller scale, this is what happens with algae blooms before they run out of resources and die off back into equilibrium with their environment.
The only reason complex creatures can even exist is because of genes made to restrain this behaviour in an organism's own cells, turn those off and you get the cellular equivalent of an algae bloom in your body.
Even then, plenty of organisms do that very same thing, like the rabbit swarms in Australia or Locust swarms in various parts of the world.
Nature doesn't aim for infinity, but it's not not aiming for it either. If the environment allowed, that's what would happen.
The sun is part of our closed system. It won't last forever, and without it no life will survive, and even if it does, the remaining resources needed to survive are fundamentally limited on the scale of eternity.
The assumption of the infinite is not an axiom of life but of the philosophical principle of Will. Which is fine if you embrace paradox and assume a will that is sufficiently exercised can live forever - and I see how biology could become a model for such an idea. But it's not intrinsic in biology. That said, the idea of infinite repetition or perpetuation of the finite is no problem at least from a Nietzschean perspective...