Our current theory that what space is is special relativity. General relativity connects space and matter. So no space isn’t the lack of stuff, stuff just may or may not be in space.
You solve the Einstein field equations for homogeneous matter distribution and you get expanding space. Similarly of how things aren’t stationary, their fundamental nature is to move and change in their motion is the interesting thing, the fundamental nature of space is to expand (or contrast).
So no, space isnt the “lack of matter” as you still have space when you have matter.
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