Theists: What is the most compelling argument you have heard for Atheism?

[Neo-Scholastic]

That's like asking how the lottery winner knew to choose just those numbers.  We're living in the 'winning ticket' and are part and parcel of it.

Your scenario is similar to Borges's when he said that the in an infinite universe all possibilities would be exhausted. The key word here is possibilities. A lottery result will never be "FISH." Now it could be that unrestricted chance could produce an infinite number of cartoon worlds or world's made entirely from LEGO blocks. That stance is a very high price to pay. At any moment our world could become absurd too! Even if this particular world was created by chance, it would still be constrained by metaphysical laws that are the ultimate source of the fine-tuning needed allow one permutation with life in it.