Space is a volume not occupied by matter.<quoted text>
The that sticks out here to me is this.
"Space and matter can't occupy the same volume."
What? Um "Space IS the volume" and matter occupies it or not.
But there is no space or any volume of it , we know of... not occupied by at least some matter . No matter how sparse the matter is.
The space was created with the makings of matter.
Picture a stream of space forming a spinning ball. It has pi to deal with. The ball is bigger than the volume of the stream of space it is formed from. But it's axis pulls in other space on one pole and out the other. This forms matter and its combos.
Matter fluffs space up as it is formed, increasing volume. Expanding space. The motion of space bangs against the walls of what the universe was formed in, expanding the universe.
For space and matter to occupy the same "space", then "space" has to be a complete void. Then you will have no volume. No nothing.
It's a seed that turned into a plant. Or an embryo that is still growing.