Catholics as a group don't "ignore all the counterarguments". So for example, Ed Feser recently published a book presenting five arguments for the existence of God (https://www.amazon.co.uk/Five-Proofs-Existence-Edward-Feser/...). The book responds to the various counterarguments that atheists and agnostics usually make to these arguments. You might not be convinced by the responses, but the counterarguments are not ignored.
Again, I am not trying to argue here that Catholicism can ultimately be rationally justified. I'm not a Catholic, and it's not particularly important to me whether it can or can't be. But it's unfair to caricature Catholics as a group as irrational faith heads (though no doubt some individuals may meet this description).
There are an abundance of philosophical arguments. In our day, we often use the term science to refer only to the natural and social sciences, ignoring the formal ones, e.g. pure math, logic, and philosophy. The natural sciences can lead us to questions that it cannot answer satisfactorily, e.g. "Why is there something rather than nothing?" These questions are more abstract and rely on logic and well thought out arguments more than the sheer weight of physical evidence.
There are lots of philosophical arguments for God's existence. I've seen as many as 20 distinct arguments thrown about. Edward Feser recently published a book in which he writes about 5 of his favorites. However, arguments for God are manifold and go back to ancient Greece. Aristotle argued that there must be what he called an unmoved mover, a point at which causality has its source, otherwise there would be no source of anything, no reason why anything existed. Without reason undergirding the world's existence, how can we believe that anything has a rational explanation? Thomas Aquinas saw in Aristotle's unmoved mover a closeness with the theology of the Christian God as Creator of the world, and presented Aristotle's arguments, among others, as a proof for the existence of God. He listed in his great work, the Summa Theologiae, five so-called proofs of the existence of God. These are not proofs in the way in which we usually use the term in the physical sciences, but more similar to the way it is used in pure math: arguments that demonstrate that it conceptually must be so. As such, most modern scientists refuse these proofs as merely hypotheses, submitting them to an entirely different method of inquiry, one which is woefully incapable of properly addressing the question at hand.
When it comes to the basis for belief, Christians, Jews, and Muslims all hold the history of their faiths, contained primarily in their Scriptures, as further proof of God's existence, as the physical evidence that modern critics demand. With records of how God has made his presence known among his people, and even made himself physically manifest (this is particularly Christian), faith is not blind, but informed by a recognition that history and philosophical inquiry both lead to the conclusion that there is a God.
Tl;dr: Philosophy and history.
Feser's Greatest Hits:
Why Is There Anything At All? It's Simple
So You Think You Understand the Cosmological Argument?
Cosmological Argument Roundup
The New Atheists and the Cosmological Argument
The Road from Atheism
Adventures in the Old Atheism, Part I: Nietzsche
Adventures in the Old Atheism, Part II: Sartre
Classical Theism Roundup
*Five Proofs of the Existence of God *
If you are truly interested in learning about the proofs then I could recommend a great book to start:
If you want to take a look at what I'm reading that specifically addresses your objection, page 61 of this book: https://toptalkedbooks.com/amzn/1621641333
Addressing your last question first: It is always good to hear someone out, no matter who they are or what they believe.
Some reading recommendations:
Start with the bible sections I've listed below, then move on to whichever of the books I have listed sounds most appealing to you. I don't want to bog you down if you don't have the time. (I personally would start with Feser)
Matthew 16:17-19 would be a good place to start. Then Isaiah 22 would be a place to see where that fulfillment in Matthew is met. As well as John chapter 6. These won't necessarily give you inclinations to believe in God, but they will give you the sense that if you believed in Christianity, then Catholicism make the best case over all other christian religions. To give you more context you should google Catholic sources for commentary on those readings.
Beyond the bible:
Five Proofs of the Existence of God by Ed Feser
The Case for Jesus: The Biblical and Historical Evidence for Christ by Brant Pitre
Jesus and the Jewish Roots of the Eucharist: Unlocking the Secrets of the Last Supper by Brant Pitre
Theology for Beginners by Frank Sheed
First and foremost. God loves you. This is the most important thing anyone here can relate to you. Just know that God loves you and He made you with a purpose.
Now, to make inroads to the Catholic faith, you need to approach this in a logical manner. Since you're coming from the perspective of an atheist, the common approach to recognizing the truth of the Catholic faith is as follows.
Does God exist?
Has he revealed himself?
How do we know?
There are many classical arguments to answer the first question. The most basic and simple argument is a thought experiment that goes as follows. Where did I come from? If I was created, or caused, then who created me? If I say my father created me, then who created, or caused, him? If his forefathers created him, then what led to their existence? If the universe cause their existence, then what caused the universe? Continue in this manner, and the result is an infinite regression of causes. But an infinite causal regression is impossible because we can't have infinite temporal relapse. In other words, there must be an "uncaused cause," or what Aristotle referred to as an "unmoved mover." This primal cause is the cause of everything else, because everything regressed back to it, and we say it is infinite being, because everything that exists can trace its existence back to this one being. The unmoved mover, as such, is God.
You can read more about other proofs for the existence of God from the following author (who also is a former atheist, turned Catholic).
Once you have convinced yourself that the universe cannot be infinite and must therefore have an infinite Creator, you can perform another thought experiment. If the Creator is infinite in being and all powerful, can he, and has he, revealed himself to mankind? Well, if the answer is "yes," then we must search for the evidence of that revelation, and by nature of the history of human perception, we must find such a concrete revelation in the annals of human history. We read the Bible for the evidence of this revelation. In particular, the resurrection of Jesus brought to its completion the fullness of this revelation. Even secular historians agree on several main aspects of this story. A) Jesus died by crucifixion under Pontius Pilate. B) Early Christians testified that they saw the risen Jesus in the flesh. C) Many of these witnesses were martyred for proclaiming this. To summarize the argument for the resurrection, we look at what the alternative possibilities are and rule them out to draw the conclusion that the mainstream story is most plausible and therefore the accurate one. Gary Habermas, an evangelical Christian scholar, has made good work on this subject.
Finally, you need to come to the recognition that the Catholic Church has the fullness of the Christian faith. To be brief, we as Catholics believe that Jesus Christ established this Church during his earthly ministry and made Peter the first Bishop of Rome (the Pope). Suffice it to say there is supporting Biblical scripture for this, and ample evidence that the early fathers of the Church regarded the Catholic Church as the one true Church, and further evidence that they observed the same traditions we Catholics carry on today. The supporting literature and apologetics for this subject are numerous, and I won't yet post them all. For starters, you could read Trent Horn's book. He's a relatively young Catholic apologist, and I really like his approach.
Read it , if you're curious.
Sorry about what happened, here are some suggestions:
I would recommend praying. Then, you might want to look into Edward Feser, William Lane Craig, Alvin Plantinga, and Reginald Garrigou Lagrange.
Here is a book I heard a lot of good things about:
Specifically for praying, the Rosary is very good:
Here is a very good video:
Believing in God if understood properly is not illogical, and warranted too, but logic is not enough. God is above our minds, and therefore our minds cannot build a ladder up to the true God on their own. In the end, we are imperfect beings and need revelation, which God has given us.
Now, if you think about it, it makes sense that religious people are happy from a Christian point of view. God wants people to come to Him, and so doing so will feel natural over time.
This is a repost of mine, but I have an Aquinas 101 reading list:
A great intro would be Aquinas by Ed Feser. It is more about the five ways and Aquinas’s arguments for the existence of God, but those are barely even scratching the surface of the surface of his thought. He was truly brilliant.
Reality: A Thomistic Synthesis by Fr. Garrigou-Lagrange is another great introductory work that covers just about all aspects of Thomism.
My Way of Life is a more poetic approach to the Summa written by three Dominicans who also cover just about all aspects of his thought.
And the man himself is actually pretty accessible, especially once you understand the basics of Thomism and his metaphysics. I find Summa Contra Gentiles a much easier and less intimidating read than the Summa Theologica. I think if you skim around and just read the questions you’re interested in you’ll agree.
Oh and it can be a bit dry, but I find St. Thomas’s commentary on John to be a beautiful and awe-inspiring exegesis of the best Gospel. It is also exhausting and wordy, but well worth it.
An addendum I’d add to this is another book I finished recently by Feser, called Five Proofs of the Existence of God.