the vast spans of time for the statistical likelihood of certain events
But that one is highly debatable, as we have zero real idea about the timescales involved in making these particular discoveries. Indeed, we have zero real idea about how long it takes to invent an A-bomb after you invent your first thing (let's pick fire for the starting line marker, since although that's awfully human-centric, it demonstrates that we have no means of telling even how long human
cultures would take to invent the A-bomb, apart from our woefully insufficient statistical sample of one case).
For all we know, ten thousand years of civilization is more than enough for inventing everything that can be invented, or ten billion is way too little. Furthermore, we currently put our full faith on the principle that the universe is pretty much the same everywhere, so the issue of resources or prerequisites (be they physical or law-of-nature sort) shouldn't really arise...