Apparently, dating cave paintings is quite difficult; carbon dating requires the destruction of at least some of the painting and can give quite a range. Also many paintings use pigments that don't contain carbon.
Sometimes bones, fires and other signs of human habitation are found in the caves that can also be dated but you then have to assume that those inhabitants also made the paintings.
They also use uranium dating as sometimes calcite forms over or under the painting. (The beginnings of stalagmites). QI
Now, the Catholic position is also that evolution explains the origin of the body but not the mind, but that's quibbling. The fact remains that the official position of one of the largest religious sects on the planet is that evolution is the only answer we have.
No, it's not a fact. The Catholic Church doesn't have an "official position" on evolution and it doesn't teach that "evolution is the only answer we have."