Outside of time, would you say? My impression… and again, I’m not a classicist, I’m going off my Latin dictionary and memories of Latin class… is that “ex” would mean more like “out from.” So maybe the word “extra” would be good… that’s “outside of,” and even “beyond” and “free from.” Which sounds like it might be what you’re going for. That would be “extra tempus.”
There are, however, additional words for time, and I’m not sure if any of them might have better connotations for your purposes. “Tempus” is looking like it might be used more for instances of time rather than big eras, though it can refer to an age as well, so I’m not sure. Aetas is another word, which seems to refer to times of life, and eras… “extra aetatem” would mean “outside of an era”… that phrase does have results on google, but I’m not able to tell how it’s being used in context, there. That might fit the meaning for your purposes. “Aeternitas” is a related word, meaning “eternity,” hence “extra aeternitatem”=“outside eternity.” “Aevum” is another word to consider… it can also refer to eras of time, time in general, and eternity, and apparently took on connotations in medieval Christianity to refer to the time between human time and eternity, which would be the timeframe of angels… so if you’d like to think of your character as existing outside of eternal time, in a rather poetic way, maybe you would want “extra aevum” as your translation.
I’d be happy to be corrected by anyone with more knowledge on the subject… this was a fun research project, anyway