No, not literally…presumably. You believe that the radiation you look at is that old, because you measure certain wavelengths and study ladders, but you can‘t really prove it. Proving that something is 13 billion years old is beyond the capabilities of us apes, at least at this point.

Can you really prove anything beyond your own existence? Descartes says no. Maybe all your senses are just an illusion.

We know that light has a finite speed. We've measured it.

We know that speed is independent of the relative velocities between the litter and the observer. Again, we've carried out experiments and measured that as well