Growing up made easier
We already uncovered that science cannot be the only source of truth. Indeed, mathematics and philosophy are equally valid ways of discerning what is true. Faith/religion is the same way. In fact, the Catechism of the Catholic Church notes:
Faith and science: "Though faith is above reason, there can never be any real discrepancy between faith and reason. Since the same God who reveals mysteries and infuses faith has bestowed the light of reason on the human mind, God cannot deny himself, nor can truth ever contradict truth."
"Consequently, methodical research in all branches of knowledge, provided it is carried out in a truly scientific manner and does not override moral laws, can never conflict with the faith, because the things of the world and the things of faith derive from the same God. The humble and persevering investigator of the secrets of nature is being led, as it were, by the hand of God in spite of himself, for it is God, the conserver of all things, who made them what they are."
In other words, if science and faith/reason/religion both pursue objective truth, they cannot come to different conclusions. It is simply not possible. Therefore, if there is a perceived conflict between faith and science, so too there must be a corresponding misunderstanding in faith or in science.
Further, it is worth noting that faith and science cover entirely different spheres of knowledge: faith is concerned with the spiritual realm and with what ought to be, whereas science focuses on the physical realm and what exists therein.
God isn't scientific (strictly speaking). That is to say, because He is outside of space and time, He cannot be definitively detected by science (whose realm is things inside of space and time). But that doesn't mean that He doesn't exist; we've already shown He does. Additionally, He revealed himself by sending Jesus Christ into the world (but more on that later).
In addition, just because God is outside the world does not mean that He is not intimately involved in it. Indeed, He reveals Himself through private revelation and through miracles.
Catholics are free to believe that the Big Bang occurred. In fact, a Catholic priest was the first to propose the idea of the Big Bang.
Other Christian denominations believe in Young Earth Creationism, which holds that the earth is only 6000-10000 years old. Such an idea is taken from a literal reading of Genesis (a book which was never intended to be strictly literal; more on this later). However, Young Earth Creationism is itself a young idea, appearing for the first time in the early 1900s. Surely if the Church were to believe that Genesis was to be read literally, and that the earth is young, it would have come up in the preceding 1900 years.1
Indeed, a devout Catholic would recognize the inconsistencies in Young Earth Creationism. To hold to such a view would require rejecting objective scientific fact, which Catholics are never called to do.
Likewise, Catholics are free to believe in evolution. Again, science has shown evolution to be true even on small scales2. Indeed, Genesis's description of creation (while not intended to be taken literally) does appear to parallel the evolution of species (namely, that earth was created, then the oceans, then life in the oceans, then life on land and in the air, etc.).
Note, however, that Catholics do believe that a single set of parents, Adam and Eve, were given human souls. These souls were not evolved.