The arrow of time is conventionally attributed to entropic gradients and low-entropy initial conditions. We argue that this account is insufficient. The arrow of time is the cumulative expression of irreversible processes operating at every scale, from pre-geometric fluctuations preceding the Big Bang to the large-scale architecture of cosmic evolution. In this framework, the Big Bang is not an absolute origin but a transition threshold within a deeper, pre-geometric regime. The pre-existing state—whether void or near-void—is not a sta-ble absence but a regime of maximal ermissivity. It spontaneously generates transient distinctions, most of which collapse. Each col-lapse, however, leaves behind topological invariants: purely relational structural traces that persist independently of any material substrate. Through ontological selection, a prebiological form of Darwinism, successive cycles inherit these accumulated constraints, rendering each subsequent configuration more stable and more probable than the last. The void is never fully annihilated; it persists as an active and productive frontier, perpetually countered by the topological memory of prior distinctions. This paper shows that the first distinction itself arises from a logical necessity—a minimal self-referential loop within pure indifferentiation and that the same selective logic is self-similar across scales,manifesting even in the extraordinary robustness of extremophiles and in mathematics as the most stable sediment of ontological selection.Complexity does not defeat the void; it transforms it into the very boundary condition that makes further structure possible. Irreversibility, memory, and ontological selection thus operate as unified principles, closing an ontological loop in which the arrow of time and the timeless forms of mathematics stand as the two universal invariants of any reality that has ever emerged from the void.