Your argument is not defending your position.

If we say the Big bang is true, and it's the creation of all matter. That would include the constituent elements of matter. Even if some elements have a longer lifespan than others, that doesn't speak to when they were created.

It's perfectly possible there's a different model, the better represents reality, that would allow for something to exist before the Big bang, but that would not be the Big bang theory. That would be a different theory, if we're working with the Big bang theory then nothing existed before it.

Except the big bang is the start of both space and time, so nothing in the universe could be older than the universe because there's no time to speak of (not to mention the space for it to exist).

The moment after the big bang is called the Planck epoch. I just learned this from Wikipedia "In this stage, the characteristic scale length of the universe was the Planck length, 1.6×10−35 m, and consequently had a temperature of approximately 1032 degrees Celsius. Even the very concept of a particle breaks down in these conditions. A proper understanding of this period awaits the development of a theory of quantum gravity.". I don't really understand this, but it seems the early universe wasn't conducive to particles. Even if it was, they wouldn't be atoms. They'd just be quarks.

All of our physics breaks down at the singularity before the big bang, so assuming quarks that are around today existed then is just that, an assumption.