Are there any grounds for thinking that the distribution of matter in the universe is unbounded?

Even though we can make no observations beyond the cosmological horizon, I think people tend to picture a universe that is either homogeneous to infinity, or possibly having spacelike slices that are closed manifolds with homogeneous distributions of matter. Is there any reason other than the Copernican principle to think that this is true? Suppose an infinite universe, with all matter at the present Hubble time being contained in an exaparsec-radius ball. We would only see a part of that so small that any isotropy from density declining towards the boundary would be undetectable. I can’t think of any way to distinguish that from an infinite universe.

I ask this question because, depending on your choice of coordinate system, such a universe would be precisely the “big bang as an explosion into empty space” model that many people have but is generally treated as wrong. And it would even be meaningful (although undecidable) to say that the center of the big bang was in a specific direction from here. Or is that wrong?

My take on this is that there really aren’t any reasons beyond general considerations like the Copernican principle to reject the exaparsec ball, but that those are probably good enough. But I wanted an expert view.