When you talk about what is the rate of a clock, say, near the surface of a black hole, it’s going to be quite different from the rate of a clock here on Earth.

When you talk about what is the rate of a clock, say, near the surface of a black hole, it’s going to be quite different from the rate of a clock here on Earth. So there isn’t even a common time in the entire universe. Well, isn't there a common time for the entire universe? If we ignore being near massive objects, then observers travelling with the expansion of the universe - i.e. those those who don't see a dipole in the cosmic microwave background (CMB) - then the redshift of the CMB acts as a kind of clock. With the usual cosmological assumptions of isotropy and homogeneity, then there's a big clock for everyone to use.