I will prove to you that God exists

[Thumpalumpacus]

Here is a summary of Victor Stengers book.

One of the key arguments presented in the book is the problem of evil. Stenger asserts that the existence of unnecessary suffering and evil in the world is inconsistent with the idea of an all- powerful and benevolent God. He argues that if God truly exists, he would not allow such suffering to occur.

That's a theological argument. How does an atheist use theology to make an argument against the existence of a Creator?

Using the Christian definition of God against it is actually a strong point, by pointing out the contradictions inherent.

You may or may not have heard the phrase, "For the sake of argument". It's a qualifier to announce that while one doesn't agree with a premise being advanced, one will use it in order to demonstrate its own weakness. It's implicit in Stenger's argument here.

So to answer your question, that's how an atheist uses theology to argue against the Christian god.