So MoK is talking about only 'things' (objects). The universe is not such a 'thing', so the conclusion from the OP is relevant only to objects, not the universe, per this restricted definition of 'nothing' to mean literally 'no thing'. — noAxioms

The universe is a collection of objects so OP applies to the universe.

Lemaître was opposed to mixing science with religion although he held that the two fields were not in conflict'. — Wayfarer

I read all that, and understood it enough to glean the point, the avoidance of applying the rules of one sort of being to another. A list of the 5 levels would have been nice.

As for Lemaître's comment, it was the church's open declaration of conflict with science that originally drove me away from my church upbringing, to flee to places like this.

don't have any argument to show that the whole is filled by material — MoK

Not one for the cosmological principle then, eh? It is something assumed. We have limited sight distance. No light emitted more than about 6 GLY from here has ever reached us, but as far as we can see, it looks the same in every direction. The implication is that if you were on one of those other distant places we see, they'd also see the same stuff everywhere.

FWIW, there are places that are (relatively empty) and we can see them. The Dipole Repeller is such a place, it having negative gravity which flings any nearby galaxies away, same as would happen if you pulled up in one place on the rubber sheet analogy.

The universe is a collection of objects so OP applies to the universe. — MoK

That doesn't change the universe into an object itself. The collection hasn't the properties of an object for instance (a center of mass just to name one).

A list of the 5 levels would have been nice. — noAxioms

That doesn't change the universe into an object itself. — noAxioms

I didn't say that the universe is an object.