That’s where the explosion analogy breaks down. At the start of the Big Bang, the universe was in an incredibly hot and dense state. If (as is commonly suspected) the universe is infinite, it was already infinite at that moment. The “bang” in question was an extremely rapid expansion of space in that hot, dense state.

The same stuff occupied the space in the universe then as it does now, just space has expanded by an incredible amount so that everything is farther apart than it used to be.