Can we know the existence of God by our reason?
Yes. Human reason can know God with certainty. The world cannot have its origin and its destination within itself. In everything that exists, there is more than we see. The order, the beauty, and the development of the world point beyond themselves toward God. Every man is receptive to what is true, good, and beautiful. He hears within himself the voice of conscience, which urges him to what is good and warns him against what is evil. Anyone who follows this path reasonably finds God.
From Catholic Youth Catechism (question 4)