It really depends on one’s intelligence. It really does. I never knew the word “pater” was Latin for “father,” but I was familiar with the sound of the word, and that it had something to do with “father.” I never knew that “noster” was Latin for “our,” but I was familiar with the sound of the word, and that it had something to do with being together amongst others, so I inferred it to mean “our.” I never knew the words “filio” and “filioque,” but I knew the English word “filial,” so I drew the conclusions.
Personally, I have a knack for grammar and vocabulary. I’m good at understanding foreign languages, especially when they’re written. I have NO IDEA why, but I just get the “feel” for the language, then my mind goes nuts making tons of connections to English, then I can at least partially understand a text.
If you know your own language really well, and at least know extremely rudimentary rules of other languages (in this case, Latin) like common suffixes and prefixes which will distinguish nouns, verbs, etc. (I know I’m not being technical here, but you get what I mean), then it’s not so hard to begin to understand related languages.
I’ve never taken a Latin class in my life, nor have I ever looked at a Latin textbook, but I can understand the majority of a High Mass (as it’s sung out loud), and I’ve only been interested in Latin for about four months. And it’s not like I come home every day and study this stuff. And, I’ve only been to two High Masses, and four EF masses total.