For the universe to expand, the universe needs to be a something.

It isn't.

Matter is moving outwardly. The universe is not.

Universe is not even a scientific term. It is a word borrowed from regular language.

Other words:

Omniverse (better, more correct than Universe)

Whole-All (notice how this is a double term)

The universe includes all there is, seen and unseen. It is a collective term and can include parts that contradict.