If you put a lot of energy into a small place, you end up producing particles. We know this and in fact we can do it in particle accelerators. We understand how this happens with a very high degree of precision. The big bang was, essentially, just a huge amount of energy in a tiny place. So according to everything we know about particle physics, lots and lots of matter-antimatter pairs should have been produced. We also know there are some tiny violations of matter-antimatter symmetry that might have caused only one kind to remain after things spread out and cooled down. We know this because we have observed the weak nuclear force violate that symmetry in experiments. But these violations are so tiny that it seems a truly ridiculous amount of matter was necessary in the first place. The only assumption here is that what we currently know about particle physics and quantum field theory still holds true somewhat close to the big bang. I understand that this might seem unsatisfactory on many levels (and it still is to many physicists), but assuming that only one kind of matter was created in the big bang would require a completely new mechanism beyond any currently known physics.
The proportion of matter and anti-matter depends on the temperature.
With increasing temperature, the thresholds of generation for various particle-antiparticle pairs are exceeded, so those kinds of particles and antiparticles are generated in collisions and become a component of the matter of that temperature.
At very high temperatures, matter is composed of almost equal quantities of particles and antiparticles, of a very large number of kinds.
With cooling, some particle-antiparticle pairs are no longer generated and the existing are annihilated, so they cease to be a component of matter.
When the temperature diminishes to a few tens of MeV, then the only particle-antiparticle pairs that remain are of electrons and positrons, while the rest of the matter consists only of free protons, free neutrons, photons and various kinds of neutrinos.
With further cooling, protons and neutrons begin to bind into nuclei, i.e. nuclei of isotopes of hydrogen, helium and lithium.
Then, with even further cooling, the temperature becomes insufficient for generating positrons, so the huge number of existing electrons and positrons annihilate with each other, leaving a much smaller number of electrons, which is equal to the number of protons (free or bound in nuclei of deuterium, He isotopes and Li isotopes), and the amount of charged antiparticles becomes negligible.
At the stage when the temperature is a few tens of MeV and the variety of the particles composing matter is minimal, any memory of what may have happened at other temperatures is erased.
Thus, we cannot extrapolate the Big Bang towards higher temperatures, because there is no evidence of what may have happened before, e.g. of whether higher temperatures have ever existed. The existing evidence could also be matched by a cooler earlier Universe, which has been heated somehow up to a temperature of a few tens of MeV, decomposing any previous matter.
Our astronomical data is consistent with the visible Universe starting at a temperature of a few tens of MeV and high concentration, then cooling and expanding from that state, e.g. this explains the observed chemical composition of the celestial objects.
It can be fun to speculate about what may have happened before that, but it must be kept in mind that for now there is no way to verify any theory that attempts to model earlier stages, e.g. there is no way to verify if the Universe had ever been hotter than a few tens of MeV, i.e. if there have ever been any other abundant antiparticles except positrons (and antineutrinos, which remain abundant even at the present low temperatures, but the nature of antineutrinos is not well understood even today, as anything else that are named antiparticles participate in electromagnetic generation/annihilation reactions with their particle correspondent, while the exact differences between neutrinos and antineutrinos are not clear).
You're basically entering cyclical universe model levels of speculation at this point, which is even wilder. Because you only delay the production of the original matter that seeded "our" universe to a point earlier in time. But given everything we know about particle physics today, it seems at least weird that matter-antimatter is such a well preserved symmetry on small scales and so little on large scales. But if the LHC or future colliders found a highly CP violating process (cough SUSY cough) just above the energy scales we can access right now, everything would fall into place pretty neatly.
There is no evidence for a cyclical universe, like there is no evidence about anything else that could have happened before the matter of the observable present universe had a temperature in the range of tens of MeV.
Like I have said, one can hypothesize that before that state when the temperature was in the range of tens of MeV the matter had been even hotter, or on the contrary, that it was cooler, but either way there is no evidence for any earlier conditions and whichever extrapolation is chosen it eventually reaches things that cannot be explained, e.g. if the evolution had been cyclical, why it has reversed, or if the matter was hotter, why it was surrounded by an empty space, allowing expansion and adiabatic cooling, or if it was cooler either whence the extra energy came or what could have caused an adiabatic compression.
So my opinion is that for now any discussion about what could have happened before the moment of time when the temperature was in the range of tens of MeV and there were no other antiparticles besides positrons and antineutrinos and no other abundant hadrons except free protons and free neutrons is a waste of time, because being unverifiable any theory about that time is non-scientific, unless someone would discover a really new theory about the structure of matter, significantly better than anything that has been proposed during the last century, which could offer additional insight.
