The universe is not uniform/isotropic at large scales
I don't think that, in this regard, you can say much more than "the universe is not isotropic across space-time".
The cosmic microwave background gives you a physical realization of just that (but of course only approximately so), at least as far as cosmologists are concerned. The rules of relativity of course still apply, making this particular synchronicity convention just one of many others...
An event is a single point in spacetime, whereas photon decoupling happens everywhere, defining a spacelike hypersurface we use for synchronization (in the idealized scenario).
Subsequently, the CMB allows us to single out a particular reference frame (the one where it looks isotropic) and provides a measure of expansion via its redshift/temperature which we can then translate to cosmological time (ie time since the big bang as measured by an observer following the Hubble flow) via our cosmological models.