I wonder if we are asking the right questions…
My questions would be, what is the definition of the “being” that an atheist is denying (when he uses the term “god”)? Or, what is the definition of the “being” that a theist is admitting to?
I would venture a guess that the “being” the atheist is denying, or that “being” that the theist is admitting, are nowhere near the Being we, as Catholics, call “God”.
If we know the definition or descriptions of the god they reject or the god they would admit, we might very well understand that rejection into atheism is appropriate, or keeping the theistic view is appropriate in many cases.
As Catholics, we are not trying to propagate the belief in the god which the atheists define as our god. Instead, like Paul in Athens, I think our goal is to bring a revelation that re-aligns their view of God with the ultimate goal they have for life, just as Paul introduced knowing God to that people which wanted to know what they thought to be unknown (unknowable?). We know the human soul is looking for the True, the Good, the Beautiful. In a way these are unknown, the unknown God, for the atheist and theist, even though they have other gods they reject or admit.
Not an easy task, and it sounds somewhat poetic or rhetorical at this point, but what do you think of this line of thought? I have to believe there is another way of approach to them besides proofs. Just like us they learn through their senses, they have appetites and will, tending toward union with what they perceive as “good”. God “wooed us” with his apparent goodness. Can God be presented likewise to them? After we believed, we came to see the reality of the absoluteness of God and our own being in contingency. But we were shown something desirable first; only then did we come to understand it.