The universe, by definition, is all there is. So there is nothing outside it, not even space, since if you extrapolate the present expansion of the universe back far enough in time, you end up with a tiny space, just after the big bang occurred.
So, from a personal perspective, I ignore the ordinary definition of the word space, as in the "space between New York and Washington". That's OK for small distances, but on the scale of the universe, which is what your question is about, I would prefer to think of space (actually spacetime) as a record of the relationship between the physical objects within the universe.
I am not sure this is a view widely shared, as it could be seen as a way out of answering your question, however it it is the only way I can think of to address it, whilst keeping in mind that the universe is ALL there is, including spacetime.
After all, what actually is " Space". It's nothing, no thing, so you can have some leeway in your definition of it :)