Type II supernovae have hydrogen. Where did the hydrogen come from if that is the first element used up in the star's life cycle? Also if our solar system was seeded from an ancient supernova where did the sun's hydrogen come from?
Good question - the answer is that stars are not in general well mixed - or rather, the nuclear-burning core is not well-mixed with the rest of the star.
That means that a star will finish hydrogen burning even when about 80% of the hydrogen in the star is still available, but is situated outside the core and cannot be mixed into the core (or at least not very efficiently).
By the time a type II supernova explodes, a large fraction of its envelope (the region outside the core) is still hydrogen.
The Sun's hydrogen comes from the big-bang. Hydrogen is not manufactured in stars, it is a raw material that was created in the first minutes of a hot big bang 13.7 billion years ago. The same is mostly true for helium, but the heavier elements in the Sun are the products of nucleosynthesis of the billion or so stars that lived and died in our Galaxy before it was born. The material that they eject through stellar winds and supernovae of all types is thoroughly mixed into the interstellar medium.
Where did the hydrogen come from if that is the first element used up in the star's life cycle?
Hydrogen is indeed the first element that is fused into helium in the core of a star -- but not necessarily the entire star. For a star to consume all of its hydrogen would require the star to be fully convective. Only the smallest of stars are fully convective. Even our Sun, which is an intermediate class star, is not fully convective.
The only kinds of stars that can undergo a core collapse supernova at the end of their lives are very massive stars. These very massive stars have convective cores while they are on the main sequence, but that convection does not span the bulk of the star. These very massive stars are instead surrounded by a non-convective outer shell that is mostly hydrogen that is never involved in the star's fusion processes. This outer shell of primordial hydrogen is the source of the hydrogen lines in type II supernovae.