Really? I did not know that this type of argument was one that is very harshly criticized by the Church’s theologians. Thanks for making me aware of that.
It’s not criticized because it’s wrong or unorthodox or bad doctrine - St Paul even uses a version of it, severely truncated, in Romans 1:19-20, and St Thomas uses it as the fifth of his Five Ways - but merely because it’s easy to criticize and not much harder to refute.
They wish to use the strongest arguments for God, because, if a weak one is put forth, how easy is it for the atheist to say, “is that the best you have?” and never try to think of it again? An atheist doesn’t want to believe in God, as the atheist doesn’t have to worry about sin or damnation. No one wants to be convicted of sin: so, when doing apologetics in natural theology, you start out strong, and then, if you’re evangelizing a learned man, built a cumulative case. The teleological argument can be useful as part of a cumulative case in some circumstances, although against physics/science types it’s useless (because you have to break down their pet theories designed specifically to keep God’s foot out of the door even when it is inevitable - such as “chaotic inflation” - first,* which is harder than evangelizing them using other arguments and methods) and is generally the one of the last you’ll pull out.
*Some scientists held to the steady-state/eternal theory even after Hubble demonstrated the Big Bang conclusively because they believed the Big Bang was too close to religious creation, and would inevitably result in respect for religious accounts of creation, which got it correct thousands of years before science did, and most philosophers kept getting it wrong (including Plato and Aristotle) until they were religious philosophers working with a revelation.
When arguing for Christianity in specific, and events such as the Resurrection, there are no proofs, only cumulative cases.
I also highly recommend William Lane Craig (Protestant) and Peter Kreeft (Catholic) for stuff on the Internet. For books, there’s Alvin Plantinga (Protestant), Richard Swinburne (Orthodox), Thomas Aquinas (Catholic), Etienne Gilson (Catholic), Edward Feser (Catholic), and many others (ask if you want recommendations for dead trees). Edward Feser is one of my favorites for beginning philosophy or natural theology, because he’s an Aristotelian Thomist.