Calculating the age of the universe
It is a common point of confusion, but an infinite universe can still have been at a unique singularity in space-time at a finite time in the past. 

This singularity is not a "point in space", since every point in the universe participated in the big-bang. It is merely a time at which the scale factor, which multiplies the separation between all spatial points in the universe,  was zero. 

So in cosmology governed by the Friedmann equation, the age of the universe thus calculated is the same whether you are talking about the "visible" universe or an infinite universe. The light travel time really doesn't come into this, because different parts of even a very large universe can be causally separated yet still have originated at the same singularity.