I am not a physicist, so I would really appreciate using a simple language for the explanation of my question. From what I understood at the early Big Bang the four fundamental forces were unified to one and the spontaneous symmetry breaking (SSB) occured causing the rise of the different four forces. Would that mean that the fundamental laws changed when SSB occurred? Or was the fundamental laws existing only before SSB?
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.