Yeah, but then it combines with stuff and is no longer hydrogen. For example, a lot of it on earth is bound with oxygen in a from known as dihydrogen monoxide. You can input energy to separate the two hydrogen from the oxygen, but it's not freely available. This is a useful way to spend excess energy to store the energy for later or to move, but not if you don't have excess clean energy.

You can also get some from things like Methane (CH4, aka natural gas). This is how most of the gas companies are producing it, and it obviously isn't clean. They like to pretend it's clean by saying using the hydrogen just produces water, but obviously the hydrogen didn't just appear.

https://en.wikipedia.org/wiki/Hydrogen_production

Some is also produced by the decay of heavy elements (helium too)

Hydrogen is the name of both an atom and a molecule, and humans are perfectly capable of creating hydrogen molecules.

You just described the same event twice. The particles formed shortly after the Big Bang came into being precisely through the formation of particle-antiparticle pairs in the energy-dense early universe.