When they say "300,000 years after the big bang" how do they count that, is that seconds in some periodic movement inside matter or radiation?
Only after the universe became transparent did these photons become free, and since they were produced roughly homogenously in that soup there are everywhere in the same quanitity: a background radiation.
Since they were not produced in a localized event, they won't have a center. But since they're everywhere, they are a sort of absolute reference for how fast you're going (actually that's a new and interesting idea for me too, pretty neat).
What you’re asking is analogous to asking where the center of the Earth is on a map of the surface, and arguing it must exist because of how things on the horizon change when you move.