Normally, if massive particles are present we can talk about the time scale set by their mass $t_C = \lambda_C /c$ where $\lambda_C = h/mc$ is the Compton wavelength.
However, their was an era during which the electroweak phase transition hasn't happened yet. During that era the expectation value of the Higgs field was 0 and hence all particles were massless. In this case, there is no universal time scale, it's undefinable. Physics during this era was simply scale invariant: $t \to at$ would result in the same. Hence, before the phase transition it's actually impossible to properly measure time.
Even then, the FLRW metric is defined using co-moving coordinates, but every particle moves at $c$ in every frame. We can't just move along with a particle because we can't find a rest frame for that particle. Moreover, as they are massless they all move on null geodesics: $ds^2=0=c^2 d\tau^2$ where $\tau$ is the proper time. From this we can see that $d\tau = 0$, so which proper time of which particle can we promote to cosmic time? None of them!
Once could construct a cloud of particles and use its centre of mass as co-moving particles, but in a scale invariant theory it's useless to measure distances. So this method also fails.
Talking about time so close to the Big Bang is highly nontrivial.