True or false: The first stars must have been made of hydrogen already in existence or in other words hydrogen has always existed?
Hydrogen, in the form of protons and free electrons, formed from Big Bang nucleosynthesis in the first three minutes after the big bang. (Before that, quarks had not yet assembled into protons, because it was too hot.) Hydrogen atoms formed 300,000 years later when things cooled off enough for electrons and protons to combine. The first stars formed about 20,000,000 years after that, after some of the hydrogen had collapsed around gravitational perturbations in the Dark Matter.
False I don't believe that true we know universe did not always exist.
Intrinsic Random Event
No. I'm no astrophysicist, but I'm fairly sure that none of the highly regarded ones believe that hydrogen is "eternal", or that there is anything unusual with regards to hydrogen and the existence of any stars that we can see based on our current scientific model of the Universe.
False, we know there was no always for the universe.
No. Hydrogen was the first element that was firmed after the Big Bang and the Universe hyperinflated and cooled down enough for energy to start converting into matter. Some helium was formed, a smaller amount of lithium and a smaller amount of beryllium. Hydrogen has NOT always existed, but there is still a lot of primordial hydrogen in the Universe.
Hydrogen was created during the first few minutes after the Big Bang.
I don't know that "always existed" is necessary, but hydrogen had to exist for stars to exist, so there were no stars until there was hydrogen. Apart from a supposedly small amount of helium, all atomic matter was once hydrogen, according to how we understand things, so there is little to no atomic matter that exists now that was not at one point hydrogen, at least in part.
Hydrogen formed early in the formation of the universe. Right after the Big Bang hydrogen was not around yet because it was too hot for protons and electrons to come together.
No. Hydrogen formed when the universe was sufficiently cool for electrons to bind to protons. Before that, it was just protons and electrons whizzing around with too much energy to bind together or stay bound when another particle collided with them. It's all about expansion / cooling / average relative particle velocity in the early universe.
Maybe. We don’t know.