Which came first: leptons or baryons? If you had a big collection of neutrons, they could decay into protons, electrons, and neutrinos through beta decay since protons are the only stable baryons. After a while, you should get hydrogen out of that. 
Assuming some process to account for baryogenisis, this would mean that the universe could start with a whole bunch of neutral baryons and generate electrons as needed without having to worry about pair production to get its leptons.
With this in mind, is there any evidence that hadrons were created first and then, in turn, created leptons (regardless of evidence for baryogenisis itself)? Or does the current theory suggest that leptons and hadrons were created contemporaneously in the very early universe?
 A: 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 .
A: The energy level/temperature in the initial universe was far too high around 2 Trillion Kelvin) to allow Baryons to be stable. There were leptons plus a quark-gluon plasma, and as temperatures rapidly cooled down, these quarks combined to form baryons.
According to our current model, leptons were here first. No temperature is too hot for the leptons. 
