Remember the Heisenberg Uncertainty Principle:
And since E=mc2, we can rewrite this as In other words, over a small enough timescales, there is some uncertainty as to how much mass there is in a vacuum. This is the source of virtual particles: matter can spontaneously appear. But it must do so in particle pairs -- matter and antimatter (ie a positron and an electron). So they will annihilate almost instantly, in a time Delta t, which for electron-positron pairs is ~ 6x10-22 seconds.
Particles that were present before inflation would be "diluted out" -- the density of particles would be essentially zero after inflation. So particles today are thought to have been produced by the energy released during inflation.
So after inflation we have a Universe filled with elementary particles and photons. But normal pair production means that they are still going back and forth between gamma rays and particles, for example:
But the universe is expanding (normally, now, not inflating), so the gamma rays are getting redshifted and losing energy. When the universe was 0.0001 seconds old, the energy of the gamma rays had dropped to the point where they could not create protons and neutrons. You could still lose neutrons when they collided with antineutrons, but you couldn't make any more: the matter content of the universe dropped, and the radiation density went up. A similar thing happens with electrons and positrons at t=1 second.
So did we just lose all our matter? Why are we here?
There must have been an initial asymmetry in the amount of matter and antimatter in the Universe: for every 109 antiparticles there must have been 109+1 particles. Wow. Ask the physicists about that one...
So we are left with lots and lots of photons and very little matter. Welcome to the radiation era.
After about 2 seconds, the density of the universe dropped enough that neutrinos stopped interacting with the matter, and "decoupled" from the thermal history of the Universe. There should be lots of primordial neutrinos running around in the Universe...
Now we have a hot universe which is a few seconds old. The energy budget is dominated by radiation, with a small mixture of protons, neutrons, and electrons. Time to start making elements: Big Bang Nucleosynthesis