Hydrogen is what you get when a proton captures an electron. The proton is one of the stable baryons you can get when a quark-gluon plasma cools and condenses. The electrons and other leptons were already in the plasma.
The quark-gluon plasma was farted out by the big turtle on whose back we all sit.
Good question. I don't have an answer, but here's another problem without an answer:
Say the universe started with the big bang (you've heard of that, right?). What was before the big bang? That's pretty hard to say because "time" is a property of space. Without space, there is no time. Before the big bang, there was no space. Hmmm.....so there is only "after" the big bang, no before....hmmmm. No time to create a universe until after the universe has been created. I'm sure you have a more satisfying answer for this problem than I can find.