We can both agree that the Big Bang happened 13.8 billion years ago but that's all, we'll still disagree about the timing of everything else. Not even the CMB can be used as an universal rest frame. I'm not a cosmologist though.

Relativity. Every path starting at the big bang to the present has its own unique clock.

These clocks can measure the difference in the flow of time between your head and your feet (and quite a lot more accurate than that)

No, we do not have an absolute reference point for time. Our best models of physics are time-translation symmetric (this is equivalent to conversation of energy via Noether's theorem), so absolute time cannot have any measurable effect. There is, however, a human made reference time scale (International Atomic Time, TAI) which is generated by the BIPM using (mostly GPS-based) comparisons of the local time scales of many national labs.