Admitted: I find it already surprising that a photon can travel for billions of years without bumping into something in a universe that has the size of current observable universe but there I guess the answer is just that the universe is really really empty.
However a friend pointed out that for photons having traveled for 13 billion years and only being observed now the not bumping into something is even more surprising: they started their 13 billion light year journey at a time that there wasn't even 13 billion light years of space available to travel through. So what happened there? Did the expansion of the universe somehow 'outrun' the photon?
I feel that some of the answers to Why is the observable universe so big? and its many duplicates might also apply here, but since the question is more or less the opposite I would appreciate it if someone could explain it in terms related to the current question.