In the context of FRW cosmology, there is no difference in the rate of time between the epochs of the evolution of the universe. You can see that from the form of the line element
$$ds^2=-dt^2+a(t)^2\gamma_{ij}dx^idx^j.$$
That is a result of the symmetries that you assume for the matter distribution (homogeneous, isotropic) and the choice of observers that you make. So the observers that follow the expansion of the Universe, which are the galaxies more or less, perceive the same time wherever and whenever they are. The cosmological time is the proper time of all the comoving observers, as it is evident from the line element.
In the case of a Schwarzschild metric and static observers
$$ds^2=-(1-\frac{2M}{r})dt^2+(1-\frac{2M}{r})^{-1}dr^2+r^2d\Omega^2,$$
it is the factor in front of dt that makes the difference and you have different time rates for observers at different positions.
There is one more point. Someone mentions the redshift and the perceived difference of the rate of time for faraway objects. That would appear to contradict what I am saying, but it isn't. The redshift effect is an observer symmetric effect. Like in the case of SR where you have two inertial observers with different velocities and each of them thinks that the others time runs slower, when both of them actually experience proper time. That is very different from the case of the static observers near a gravitating object, where there is no such symmetry. The clock of the observer that is at bigger r runs faster than the clock of the one that is at smaller r.
In simple language we do not have a Theory Of Everything (TOE) therefore any answer about the ultimate existence of specific laws is a tentative one. What we do have is a set of nested mathematical theories that fit observations mainly in the study of particle physics. These theories extrapolated to the extremely high energies at the beginning of the Big Bang look reasonable and explain cosmological observations, thus are in this sense also validated up to now.
The search for the holy grail of unification of all forces started when electricity
was unified with magnetism in the nineteenth century. Experimental measurements of the coupling constants that characterize each force , as a function of the energy of the interaction led to the following experimental observation
running coupling constants
where we see that the strength of the couplings converges for the three forces that can be studied with particle physics.
Scientists believe that as they push the energy they are able to study higher and higher (achieving smaller and smaller resolution), they will see the values of the coupling constants get closer and closer together. They believe that at the energy that was around at the Big Bang, all the forces would have had the same strength with the individual forces familiar to us condensing out as the Universe expanded and cooled. This idea is called unification .
The concept of spontaneous symmetry breaking has good experimental validation for the three forces, that they separate as the energy falls, and it is a hypothesis for the gravitational force.
In the sense that the theory is known for the three forces, below 10^15GeV, SSB is a law that exists even at the maximum limit, but it is a mathematical statement. When the TOE is found it is only necessary that its mathematical formulation converges and explains the SSB of the three forces.
We do not know if the unification of all forces happens at an energy value lower than the one available at the Big Bang or starts at the singularity. There can be models though. In the forces plot the unification is given below the maximum, at the Planck Energy . It seems a good hypothesis at the moment. The "laws" start appearing as the universe cools, they pertain to the specific energy range studied experimentally and are a mathematical hypothesis for the yet unexplored. Nature might still have surprises for us.
Best Answer
The closer to the Big Bang you look, the more fundamental are the particles that constitute the universe (quarks, leptons, etc.) - go far back enough and you reach the point where only a field description makes sense because of the curvature of the universe.
But after the 3rd minute and up to around the 20th minute, the universe had cooled down enough for nuclei to form and yet was hot enough for fusion to occur. This was the period of nucleosynthesis when the first elements in the periodic table were forged. Most of the nuclei formed were hydrogen and helium and their various isotopes but there were also trace amounts of lithium and beryllium.
This is confirmed today in the precise ratio of elements observed in the universe with the significant abundance of hydrogen and helium, and is one of the best numerical confirmations of the Big Bang theory.
Rocky planets and humans and what not however require higher elements like carbon, nitrogen, oxygen and silicon to form. These were not formed in the Big Bang like H and He. They were forged at the centres of stars and dispersed in violent supernovae explosions that took place millions to billions of years after the Big Bang.
That still is pretty wonderful - that every atom in our body has its origins in either stardust or the Big Bang.