What is the primary implication if space is truly flat and infinite?

Everything that can happen will happen an infinite number of times

A flat universe possessing infinite spatial extent carries a profound consequence related to probability and configurations. If space extends forever without looping back or curving in on itself, then the number of possible ways that particles can arrange themselves within any given finite volume—like a Hubble volume—must eventually repeat across the infinite expanse. Because there is an infinite volume available, any arrangement of matter and energy that is physically possible, no matter how unlikely, is guaranteed to occur an infinite number of times throughout the cosmos. This means that there would be an infinite number of Hubble volumes identical to our own, containing duplicates of everything we observe, though these duplicates would be separated by unimaginably vast distances beyond our current observable horizon.