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When fusion or fission occurs you get new atoms.
It's Hydrogen that's existed since the universe cooled enough for electrons and protons to make atoms. Seconds after the big bang.
That's most hydrogen.
It's never been fused into heavier elements just still sticking around and caught in the planetary part of the solar system rather than the sun itself. Or any previous suns.
There's some helium like that but most helium was formed inside suns later, and heavier elements all formed later in suns or supernovas.
Atoms didn't exist until 380,000 years after the big bang. Before that the universe was too dense for atoms to form and everything existed as a hot dense plasma where no electron could be captured by protons and neutrons. The protons that make up the nucleus of hydrogen did exist, it's just that everything was too energetic to become an atom yet.
But you don't get new protons and neurons that way right? Higher nucleei are just hydrogen nucleei that got too cozy with each other.
Don't forget neutron star collisions. Modern physics doesn't think there's enough energy in supernovae to create all the elements, so some must have come from neutron star collisions.
More like 380,000 years after the big bang you still needed everything to cool down and forces to separate and lots of other really cool stuff to happen before hydrogen could form.