We do know that the universe doesn’t need anything to expand into, and we haven’t seen any evidence that there is anything outside of the universe. Most of the theories about the outside of the universe fall into the “I can’t say you’re wrong for sure” category. We can say that space isn’t “made of anything”, and that it doesn’t need any kind of “higher space” to exist in. However, that outside is defined in terms of space, and all of space should be inside the universe. Science (and more generally: everything we can know), being based on observation, inference, and experience, can’t say much about things entirely outside of the universe.