Yet God hath placed by the side of each a man’s own Guardian Spirit, who is charged to watch over him – a Guardian who sleeps not nor is deceived. For to what better or more watchful Guardian could He have committed which of us? So when you have shut the doors and make a darkness within, remember never to say that you are alone; for you are not alone, but God is within, and your Guardian Spirit, and what light do they need to behold what you do?
(XXXVII, The Golden Sayings of Epictetus, trans. by Hastings Crossley, 1909)
It is common Catholic belief that each person has a Guardian Angel, similar to what Epictetus (a Stoic, teaching probably around A.D. 100) is describing here. It seems this belief that many people might nowadays think of as specifically Christian (as I had) in its origination was more broadly held, both before and during the rise of Christianity.
A simple reason for why it was more broadly held is that it’s not a belief based on Christian scripture. Rather, people have experiences which suggest to them something like Guardian Angels.