That space within matter is volume. You can measure it. Matter is like a web or a knit formed within the larger volume that space fills. Its like a foam.<quoted text>
You need to adjust your intuitions because they are leading you away from the truth. Space is inside matter and matter exists in space. The 'source' is irrelevant.
Oh, the ironies!
Space is not a void. It is a something formed with the universe. It's a binder holding the universe together. You can't pop into a void. That is like blowing a soap bubble into deep space vacuum, only with less effect.