In physics, infinity is usually a sign that our modelling of the physical situation has broken down; generally, the only kind of infinity that is allowed is the potentially infinite; this means that at any time a certain quantity is finite, but it may grow in size later.

Infinite space, however seems a possibility pn the face of it; if we instead pursue the notion that potential infinity in physics is the only possibility as axiomatic we can see that elapsed time must be finite; this means that the universe began somehow, and in some place; we can ask the question, did it begin all at once in a particular finitely bounded place, or over an infinitely bounded region, the former seems the more likely, for if it to begin over a whole infinite region seems unreasonable as this must have been coordinated somehow; so we take it as reasonable that the universe began, and when it began it was finite in extent.

When we further suppose growth is continuous, then the universe can only grow in the finitely elapsed time; this means the universe ought to be finite in scale - as said also by currently established scientific consensus.

In physics, infinity is usually a sign that our modelling of the physical situation has broken down; generally, the only kind of infinity that is allowed is the potentially infinite; this means that at any time a certain quantity is finite, but it may grow in size later.

There is a proviso: Infinite space, however seems a possibility on the face of it, as does infinite time: the antimony that you've pointed out is a classic one as also pointed out by Kant.

But if we instead pursue the notion that potential infinity in physics is the only possibility as axiomatic we can see that elapsed time must be finite; we can also say that physically, an infinite elapsed time is not credible, for how would we have reached the present moment? The error lies in viewing the past as like future, in being potentially infinite; however, the past is the past because that moment was lived through, and for that reason is finite. The future does not have that character, it is yet to be lived though, and so can remain potentially infinite.

Now, this means that the universe began somehow, and in some place with some extent; it being the universe, it must all of the place and to the extent of that place.

Further, we can ask the question, did it begin all at once in a particular finitely bounded place, or over an infinitely bounded region? The former seems the more likely, for if it were to begin over a whole infinite region this seems unreasonable as we know that cause and effect in the universe is local in character - there are no effects at a distance - creation must have been coordinated somehow; so we take it as reasonable that the universe began, and when it began it was finite in extent.

When we further suppose change, be it growth or diminution, is continuous, then the universe can only change continuously in the finitely elapsed time since it's 'creation'; and finite change from a finite beginning means finiteness at present, and hence a finite universe at present.

Thus, from a reasonable set of physical assumptions we have shown that the universe ought to be finite in scale, temporally & extensively - and this is also consonant with currently well established scientific consensus (excluded speculative notions of multiverses and their like).