How are hydrogen and oxygen created?

Hydrogen, the most abundant element in the universe, was created during nucleosynthesis in the first 100 to 1000 seconds of the big bang (13.7 billion years ago) [Linky]. Shortly after that, a few other elements were created from the hydrogen: Helium, Lithium, and Beryllium.

That was it. The universe expanded and cooled too quickly for any more elements to form.

It took around 200 million years for the first stars to form. Those first stars (population III or first-generation) fused hydrogen and helium to create the 88 heavier elements, which were released when the stars died and exploded. Oxygen is one of those elements.

So, there you have it; we are recycled star dust.

Garion's response: "Cooool!"