For the regrowth effect to work, you have to lose the body part while already having the ring attuned. Ring of Regeneration states:
If you lose a body part, the ring causes the missing part to regrow ...
"Lose" is a present tense verb
The ring says "If you lose a body part" not "If you are have lost a body part". The "losing" needs to happen after the ring has been attuned, otherwise it won't trigger.
Imagine going to a bar and the bartender says "if you throw a dart into the center of the dartboard, I'll give you a free drink". Do you think they will be happy if you say "ok, give me the drink, I hit the bullseye last week"?
Perhaps as part of the attunment process the ring magically establishes what your body is like, so it knows what to regenerate. Whatever the in world explanation, it doesn't seem like it would help if you've already lost a body part before you put on the ring.