One of the things that I love about Catholicism is that it integrates faith and reason. Yes, faith is important, but it is also very possible to reach the conclusion that God exists by pure reason as well.
St. Thomas Aquinas came up with 5 very rational proofs for God's existence (purely philosophical, not theological at all):
Proof #1: The Uncaused Cause
There must be a cause for every effect in the world. It is impossible that something comes from nothing. You can't get anything from no thing. You can't say that the world is just full of causes without concluding to an original cause. Therefore, to explain the effects we see today, we must conclude that there is an all-perfect being that contains its own cause of being. It is all-perfect because only a perfect being contains the cause of its own existence. We call God "God," because that is a revealed name. You can call Him, for now, whatever you want, even the Uncaused Cause.
Proof #2: The Unmoved Mover
We see motion in the world. Something in motion cannot begin moving without something moving it first. "God," as we call Him, is the Beginning Mover.
Proof #3: Proof of Necessity and Contingency
We see things today that have not always existed, and we call these "contingent beings." In order to explain the existence of contingent beings, we must conclude that a necessary being exists. A necessary being is an independent being that has always existed. You can't have a contingent being without a necessary being. We call this necessary being "God."
Proof #4: Proof from Perfection
We see beings that exist with different degrees of truth, beauty, and goodness. For example, in the category of beauty, we can all agree that Michelangelo's painting is more beautiful than a 2nd grader's drawing. (Although I have heard the argument that this is subjective, it really is objective, to a degree. Think about it. Who in the world would say that a garbage dump is more beautiful than a sunrise?) Therefore, if a person is to judge something that is more or less true, beautiful, or good, they must be presupposing an absolute standard of perfection by which we can judge imperfect things. If we say that Mother Teresa has more goodness than Hitler, we are presupposing a perfect standard. We call this perfect standard God.
5th Proof: Proof from Design
Something that possesses the qualities of design must have a designer. The more complex the design, the more complex the designer. (There is a 500,000 to 1 possibility that the human eye could operate.) Therefore, we must conclude the existence of an all-knowing designer Who designed the complexities of the universe. We call Him God.
I hope that helped! Thomas Aquinas was a genius! I sure couldn't have thought of that.