When introducing the subject of how we may know God, the Catechism gives us a balanced picture. We can discover the fact that God is there, but this is greatly simplified by His revelation.
First, the Catechism flatly denies that belief in God is irrational.
Our holy mother, the Church, holds and teaches that God, the first principle and last end of all things, can be known with certainty from the created world by the natural light of human reason. [CCC §36, quoting Dei Filius 2]
This post isn’t the place for making a demonstration of this fact, but earlier the CCC points at how this may be seen.
Created in God’s image and called to know and love him, the person who seeks God discovers certain ways of coming to know him. These are also called proofs for the existence of God, not in the sense of proofs in the natural sciences, but rather in the sense of “converging and convincing arguments”, which allow us to attain certainty about the truth. These “ways” of approaching God from creation have a twofold point of departure: the physical world, and the human person. …
The world, and man, attest that they contain within themselves neither their first principle nor their final end, but rather that they participate in Being itself, which alone is without origin or end. Thus, in different ways, man can come to know that there exists a reality which is the first cause and final end of all things, a reality “that everyone calls God”. [CCC §31, 34]
(One might also see the five ways of St Thomas, in ST I, q.2, a.3)
But that’s not the whole story. If God may be known by reason, why do men find it so hard sometimes to believe in Him? Well, in the first place it’s hard to learn the facts even when it comes to things in this world.
Consider the case of two persons of whom one has a more penetrating grasp of a thing by his intellect than, does the other. He who has the superior intellect understands many things that the other cannot grasp at all. Such is the case with a very simple person who cannot at all grasp the subtle speculations of philosophy. …
The same thing, moreover, appears quite clearly from the defect that we experience every day in our knowledge of things. We do not know a great many of the properties of sensible things, and in most cases we are not able to discover fully the natures of those properties that we apprehend by the sense. [Summa Contra Gentiles, I.3, §4-5 passim]
We’re not smart enough to learn or understand everything there is to know about the world. If this is true when it comes to earthly affairs, how much more is it true when it comes to supernatural things!
Though human reason is, strictly speaking, truly capable by its own natural power and light of attaining to a true and certain knowledge of the one personal God, who watches over and controls the world by his providence, and of the natural law written in our hearts by the Creator; yet there are many obstacles which prevent reason from the effective and fruitful use of this inborn faculty. For the truths that concern the relations between God and man wholly transcend the visible order of things, and, if they are translated into human action and influence it, they call for self-surrender and abnegation. the human mind, in its turn, is hampered in the attaining of such truths, not only by the impact of the senses and the imagination, but also by disordered appetites which are the consequences of original sin. So it happens that men in such matters easily persuade themselves that what they would not like to be true is false or at least doubtful. [CCC §37, quoting Humani Generis 2; emphasis added]
So we see that reason is definitely (and obviously!) useful, but also that it has its limits, and that we need God’s revelation.
Aquinas, Etc. 
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