The problem is that time may not function correctly in the early universe, (say around plank time).
Another maybe more practical idea is to take the average temperature of the background radiation and peg time to the way it (or the average temperature of the universe ) cools down.
Or peg time to the Hubble flow. Since we now know the Hubble flow changes over time, you could peg a measurement of time to that.
Neither of these can give us datetime numbers for the very early universe but time may be screwed up then anyway: time maybe nonsense then.
The real problem is that we need a point of reference that is external to our own frame of reference. Luckily, we have one.
Light.
Light moves at the same speed no matter what your frame of reference is. It's theorized that the early universe was dark for a very long time because any emitted photons were absorbed by other matter, because things were so dense. After a while, matter got ionized and expansion kicked in and the universe cleared up. This was the time of the first stars.
So, we need realllly good telescopes. Fortunately they're being built. The idea is that you have to find the light from the first stars. Measure the redshift and find some type 1a supernovas from the period to give you distance. (Standard candles.) Then you have a base measurement of time.
One problem is the redshift. There was a recent paper talking about how the earliest galaxies are so redshifted by now that their light is getting lost in the CMB.
So, this is "possible" only in the sense that if constrained to be useless it would theoretically be possible, but not practical.
Awesome, let's get right on that :-)