What exactly is the cosmic definition of ‘now’ is? There is no cosmic definition of now because of special relativity, because of rate at which time flows for a particular object depends upon your point of view and your velocity. For a rocket traveling at speed of light, journey of alpha centauri might take a week. For us it would seem like 4 years. As a result of special relativity even the meaning of ‘simultaneous’ is related to your point of view
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.