Well it usually takes like a few months to up to a year to get everything settled - and once you find "the right dose" it may not be the right dose for long so you need to keep an eye on your symptoms and labs in the future too. But you're on your way to recovery once you get the right medication
Don't settle for "just anything within range" - you need to adjust the medication to Your needs (aiming to have your TSH below 2 and FT4 around midrange is a good starting point, from then on tweaking if needed to get to Your "best place").
I've been medicated for 6½ years now and I ran my first half marathon last year (maybe could've done it sooner if I had felt like doing it
) - wouldn't have been able to do it without my meds
I need to adjust my meds frequently but hey, if adjusting helps I'm ok with that