I haven't read that book, but I'd argue that it's pointless, as god is not provable scientifically (or disprovable), so it's meaningless to attempt to do so.
I never said it was impossible to think critically when you are Catholic (or any other religion). But I do believe people willingly (or unconsciously) shut off their critical thinking centers whenever many topics surrounding their religion come up.
I think you are subscribing to a view called scientism[1]. If that is so, I would encourage you to read books like "Alchemy of Finance" by George Soros [2] which contains serious arguments against that position. You could also listen to David Wood or Edward Feser on YouTube if you are pressed for time.
[1] https://en.m.wikipedia.org/wiki/Scientism
[2] https://www.amazon.com/Alchemy-Finance-George-Soros/dp/81265...
You can listen to Edward Feser on youtube for some the reasoning behind Catholic dogma.