First order logic, set theory and God

[Belacqua]

As you know, what is logically prior need not be temporally prior. 

If a logician says that space-time is logically or essentially prior to, say, hydrogen, it doesn't matter whether space-time appeared first in time and then hydrogen appeared later, or whether they appeared at the same instant.

In what way is a part of a car logically prior to the car itself without being perhaps temporally prior?

Space-time is essentially prior to hydrogen in that space-time has to exist for hydrogen to exist. If space-time winked out, so would hydrogen. 

This is different from a temporal causal chain, in which the cause (e.g. your parents) may cease to exist while the caused thing (e.g. you) continues. 

I think the parts of a car must exist for the car to exist. If the parts melted and burned, the car would disappear too. Thus, the parts are essentially prior. In this case, they are also temporally prior, but I'm not sure that's what the argument is using.

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If a is the cause of b, then in what sense would it be reasonable to imply that b existed prior to a?

It isn't reasonable to imply that.