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."
My understanding is that the age of fossils is determined by the age of the sedimentary rock they are formed and found in. But sedimentary rock consists of small particles of rock from here, there and everywhere, which means those particles could vary greatly in age. So how can the age of the sedimentary rock that fossils are found in be determined with any accuracy?