Not catching up. But reaching the destination. That's limited though, as space expands. And any place is reachable that the photon is able to reach as these parts* are not expanding faster than the speed of light.
* The whole space between start and destination, of course
versus
"I am a Ph.D. astrophysicist"
I'm confused.
In other words: How is he planning to catch up to a photon?