Sure, but postulating an infinitely sized universe (full of an infinite amount of mass) does ask the question as to why the universe would not be infinitely old?
Particularly when you get into issues like entropy, which is the only real determinant of time even existing. A finite universe has a natural direction of entropy - whereas an infinite one does not, since there's an infinite amount of mass and energy and as such no possible lowest possible entropy state.
It's actually worse then that though: an infinite massed universe by definition would contain every possible configuration of that mass somewhere within it. So you and I talking right now like this, our past and future conversations would also all be somewhere else in the infinite universe happening simultaneously.
A universe with an infinite amount of mass and energy in infinite space doesn't really have any sensible notion of past, present or future - because all possible pasts, presents and future, exist at all times somewhere within it.