Electrons and Positrons?

I think the part that you are not understanding is the gradual cooling and rarefying of the Universe as it expands. In the very earliest phases of the big bang, the Universe is much too hot and dense to allow any particles to exist for more than a femtosecond or less. In this super hot, super dense phase, electrons and positrons are annihilating each other rapidly and continuously, only to reform again and then re-annihilate over and over. Only when the Universe expands enough and cools enough does it allow for the long term formation of particles. Even then, most keep annihilating over and over, but some still unknown asymmetry provision eventually allows a few electrons/protons/neutrons to remain in existence without their corresponding antiparticles. As the Universe continues to expand and cool, these particles then form the first atoms, which then form the first stars, etc.,etc.