And it's possible to come up with a model where the universe is infinite but the visible universe is finite. In fact, I believe FLRW is one such a model Just t

And it's possible to come up with a model where the universe is infinite but the visible universe is finite. In fact, I believe FLRW is one such a model Just to clarify, FLRW is a class of models, which includes ones with finite as well as infinite space. We've been able to determine that our universe is close to spatially flat. However, that does not mean it's infinite: If spatial curvature is positive but small compared to the cosmic horizon (which is due to spatial expansion), we won't be able to tell. That said, even given finite space, spacetime can of course still be infinite if the universe does not recollapse.