There exists a standard model of cosmology, i.e. accepted as the current status of research, called the Big Bang.
This makes extensive use of the known interactions of particle physics encapsulated in the standard model., and assumes a singularity at the beginning of the universe where the energy seen in the universe now was originally generated.
I like this display of the history of the universe as understood at present.
From the hypothesized quantum gravitational state from the beginning to the end of the inflation period, it is all a model that reconciles observed behavior of the cosmic microwave background radiation data to a big bang model.
From 10^-32s to 1μs the standard model of particle physics is used, where this is a soup of all the particles in the table appearing and disappearing in pair productions, so there is a quark gluon plasma which with the expansion cooling allows the creation of stable protons. There will be also by symmetry neutrons in the mix, but they will be decaying and recreated as long as the average energy of the soup, leptons and hadrons, is enough to allow for inverse beta decay..
That is where baryogenesis is necessary, the asymmetry between protons and antiprotons , and where particle physics does not have the answer yet. Assuming it happens, then it is at the next stage, in nucleosynthesis that the neutrons are captured into stable nuclei and matter as we know it exists.
So the answer is that in the current model of the universe, leptons and quarks(hadrons) came at the same time . Stable baryons made out of quarks came after 1 ms .