If that hydrogen was previously incorporated in a star, I think it's fair to call it stardust. That's very likely, since our solar system would have formed from a relatively dense cloud of the remnants of earlier stars, with just a smidge of primordial hydrogen mixed in.
All of the hydrogen was created at the initial cooling of the big bang. In this case what I mean by primordial, is that it was never part of a larger composite object like a star.
It just means the remnants of the Big Bang that mostly created hydrogen, helium, and lithium. There's nothing particularly special about it other than the possibility that it is as old as creation because there are stable isotopes.
I also like the science behind particles like neutrinos blasting their way through everything in space and matter, even through our own bodies and cells. Every once in a while, one of those tiny particles hits a piece of DNA at just the right spot to cause a chain reaction that leads to a new minor or major mutation in the next generation. It's generally thought that this kind of physics is one of forces that drive evolution of all lifeforms on our planet.
We are made of star stuff ..... and we are and will always be affected by star energy.