[AaronFriel]

Not a physicist or even anything more than a bachelor's in anything - though this is my understanding.

Many depictions of the big bang show the entire universe - something which may not have a finite volume - collapsing to an entire point.

It might be more illustrative if you imagine when you look at one of those drawings that it is in fact "merely" depicting all of the space within a finite volume today collapsing to a particular point in the past corresponds to the big bang. Conversely, things arbitrarily close together in the big bang can be arbitrarily far away now. There is no "center" of the universe, it's more like the shriveled up balloon analogy. Draw a bunch of dots on a blown up balloon and let it deflate, everything gets closer together but no one point is the center. So it doesn't make sense to ask "where were we 12 billion years ago?" The answer is: closer to everything we can see.

This explanation corresponds to a universe whose shape has zero curvature or negative curvature. WMAP and other experiments have suggested the curvature of the universe is very close to zero, but even a slight deviation above or below has dramatically different implications.