The Catholic Church teaches that the existence of God can be known with certainty by the “natural light of reason.” 1 A very traditional set of arguments for the existence of God are the famous “five ways” of St. Thomas Aquinas.2
Some people deny that we can know that God exists, or have any rational basis for believing that he does, because God cannot be observed with the senses or detected with measuring devices. Now, it is certainly true and obvious that God cannot be known in such ways, because he is not a physical entity. It doesn't follow, however, that God cannot be known in other ways.
After all, even in the case of physical entities, there are many whose existence is known to us with great certainty despite the fact that we cannot sense them or directly observe them. For example, we know that quarks, neutrinos, magnetic fields, the curvature of spacetime, and nuclear reactions inside stars exist. And we know that the common ancestors of various species and the Pangaean supercontinent existed in the past. We infer their existence as the causes of various effects that we can directly observe. Such reasoning from observed effects to the existence of their unobserved causes is very basic in science. It does not happen by deductive proof, as in mathematics, but by what philosophers call “inference to the best explanation.” 3 By assuming that certain entities exist or have existed and that certain hypotheses are true, we obtain the simplest, most unified and coherent, most comprehensive, and most intellectually satisfying explanations of the world around us.
We can know God in ways that are analogous. As St. Paul said in his letter to the Romans, even though God is by nature “invisible,” his existence can be known “through the things that are made.” The “things that are made” include ourselves and the physical universe; and Christian tradition tells us that both of these realities point to God as their ultimate cause. In the words of the Catechism of the Catholic Church,
“[T]he person who seeks God discovers certain ways of coming to know him. … These ways of approaching God from creation have a twofold point of departure: the physical world, and the human person.” (CCC 31)
The human person, being rational and free, and having the capacity to apprehend truth, beauty, and goodness, cannot be explained solely by material causes. As the Catechism notes,
“The human person, with his openness to truth and beauty, his sense of moral goodness, his freedom and the voice of his conscience, with his longings for the infinite … discerns signs of his spiritual soul. The soul, the seed of eternity we bear in ourselves, irreducible to the merely material, can have its origin only in God.” (CCC 33)
The physical universe, according to Christian tradition, points to God primarily in two ways: by the fact that it exists and by the fact that it is orderly.
The universe did not have to exist by any logical necessity, and yet it does. Why? Why not no universe? Why not no matter, no forces, no time, no space, just blank non-existence? As the philosopher Leibniz famously asked, “why is there something rather than nothing?” 4 Whatever exists, but did not have to exist by any logical or absolute necessity, must have a cause.
And why does the universe exhibit order, harmony and beauty? Why are there any regularities and patterns at all to be found in it, let alone the extremely subtle, intricate, and sophisticated mathematical laws that physics has discovered? As St. Gregory Nazianzus asked in the fourth century, “[Even if you] suppose that the existence of the world is spontaneous, to what will you ascribe its order?” In the words of St. Irenaeus, writing in the second century, God, the Author of the universe, is the "giver of order." 5
Beyond the specific arguments mentioned above, Catholics believe that the existence of God gives a more comprehensive and coherent explanation of many aspects of the world than atheism does. As the great mathematician and physicist John von Neumann once put it, “many things are easier to explain if there is a God than if there isn’t.” We can reason to God as the “best explanation.”
1.. First Vatican Council, Dogmatic Constitution on the Catholic Faith, Chapter 2, “On Revelation”, articles 1-3. https://www.papalencyclicals.net/councils/ecum20.htm
2.. For a good explanation of St. Thomas’s Five Ways, see https://en.wikipedia.org/wiki/Five_Ways_(Aquinas)#Explanation
3.. Routledge Encyclopedia of Philosophy, article on “Inference to the Best Explanation”: https://www.rep.routledge.com/articles/thematic/inference-to-the-best-explanation/v-1#
Stanford Encyclopedia of Philosophy, article on “Abduction”: https://plato.stanford.edu/entries/abduction/
4.. “[T]he first question we can fairly ask is: Why is there something rather than nothing? After all, nothing is simpler and easier than something. Also, given that things have to exist, we must be able to give a reason why they have to exist as they are and not otherwise.” G.W. Leibniz, “Principle of Nature and Grace Based on Reason.” http://earlymoderntexts.com/assets/pdfs/leibniz1714a.pdf
5.. For these and other statements by early Christian writers about cosmic order as pointing to God, see “God and Cosmic Order”, Stephen M. Barr, Society of Catholic Scientists website, Monthly Article, September 2020. https://www.catholicscientists.org/idea/evidence-of-god
Resources for further study
“God and Cosmic Order”, Stephen M. Barr, Society of Catholic Scientists website, Monthly Article, September 2020. https://www.catholicscientists.org/idea/evidence-of-god
Thomistic Evolution: A Catholic Approach to Understanding Evolution in the Light of Faith, Nicanor Austriaco, James Brent, Thomas Davenport and John Baptist Ku, (Tacoma, WA: Cluny Media LLC, 2016), Chapter 6.
The One Creator God in Thomas Aquinas and Contemporary Theology, Michael J. Dodds (Washington D.C.: CUA Press, 2020), Chapter 1.