We discuss how universal features of multi-axion theories, that are generic in certain string theory compactifications, allow us to analyze the cosmological dynamics in typical late-time universes with collapsed structure. Random order one parameters at the GUT scale, N ~ 100 axions, and conditioning on structure formation typically yields cosmological histories consistent with observation: Vacuum decay triggers a big bang followed by inflation, reheating, radiation and matter domination, structure formation and finally a small cosmological constant. Rather than scanning over distinct theories or parameters, we are able to for the first time study a representative ensemble of all cosmologies arising from a fixed parameter choice in a theory that is complex enough to accommodate the observed expansion history anthropically. Our novel technology allows to make concrete progress in the understanding of coincidence and fine-tuning problems in a specific well understood, high dimensional landscape.