The infinite cannot have a beginning, as said in Phys. iii. But everything outside God is from God as from its first principle. Therefore besides God nothing can be infinite (ST I Q7 A2).This means that the universe is not infinite, because it was created by God: it had a beginning. However mind-boggling its dimensions are, it is not limitless.
On the other hand, there is a relative sense in which creatures may be said to be infinite.
[F]or example, wood is finite according to its own form, but still it is relatively infinite, inasmuch as it is in potentiality to an infinite number of shapes (ibid.).This could be said to be an infinity of potentiality, but that which is in potentiality does not exist really. Hence we do not say that a block of wood is infinite in any actual sense, because once it is given a certain shape, it ceases to be in potentiality to all others (of course, in the sense that it could be re-shaped, we could say that it retains a certain relative infinity of potentiality; but with respect to its actual state, it possesses no such infinity at all).