What exactly is the cosmic definition of ‘now’ is?
The cosmic "now" is well-defined: It is the time for an observer that has always been at rest in the Universe's comoving coordinates, i.e. the coordinates that expand along with the Universe. Although this reference frame is no more special than any other frame, it makes sense to use this. For instance, it is the only frame in which the cosmic microwave background is (statistically) isotropic, and it is the frame in which you'll see the same number density of galaxies in all directions.

You could (rightfully) define "now" in another frame, but it wouldn't be of much use. For instance, for a neutrino released 1 s after Big Bang, the age of the Universe is some ten thousand years, but it doesn't really tell you anything about the Universe.