This is a wonderfully knotty question that has occupied philosophers at least since Zeno of Elea in the 5th century BCE. One way of interpreting Zeno on this is to say that the problem shows that space is illusory. David Hume later, like the atomists ('atom' meaning uncuttable) seems to have thought that there must be a point at which the cutting stops, at least so far as the world of experience goes. I might say that Zeno is right that certain ways of conceiving space are flawed, including the way the problem as you pose it conceives of space--that is, as continuous all the way down, becoming just a finer and finer Cartesian grid if you will, always subject to the same sorts of properties or ways of conceiving things (like length, height, depth, etc.). It seems, however, that once we reach the sub-atomic realm these ways of conceiving things just don't hold, so that it becomes impossible to apply mathematical divisions of space. Space seems dependent on, you might say, the ability of energy to...

This gets a bit beyond my expertise, but I suppose like you I find these sorts of issues irresistible. (Kant thought that part of that irresistibility was a feature of our being rational beings, by the way. Perhaps he was right.) Anyway, I'm not exactly sure what you mean by "origins of the 'Big Bang'," but I'm unaware of any scientific theories advance any position at all on any cause or originary reason for the big bang. The bang itself, perhaps from an original singularity, is as far back as natural science goes. Indeed, in a sense, it makes no sense to speak about any time before the big bang, since as I understand it time began with the big bang, too. Now, I have encountered speculation about the big bang being one in a 'series' of big bangs--where a bang would be followed by a period of expansion, which would be followed by a contraction back to a singularity, which would be followed by another big bang. But that still wouldn't offer an explanation about why this cycle exists in the...