29 years old: when is the best time to a get hair transplant?

There's no one right answer to this question, because every individual has different needs and goals. However, the optimal time to proceed with a hair transplant is after your hair loss has stopped, or at least significantly slowed, one way or the other.
Waiting until this happens naturally is the worst way to do this because you have no idea how much hair you'll lose. It may take years, and you may reach a point where you've lost more than you can restore with a transplant.
The ideal way to do it is to be as aggressive as you can in halting your hair loss with non-surgical therapies, thereby maintaining as much of your own hair as possible, and minimizing the amount you'd need to restore with surgery.
You've tried finasteride, but that's only one option. Other options include minoxidil, low level laser therapy, and PRP. All of these are effective, evidence-based options, and you can even use them in combination with each other for even greater efficacy.
Once your hair loss is stable on a regimen that you can confidently continue on an ongoing basis, which may take up to a year, that would be a good time to consider a transplant.

Hi! So hair loss will last till patient gets 40 years old generally. It would be better if we could see your pictures and make a full analysis but in your it can be some options like: do a hair transplantation now, solve your problem and maybe you won't lose your own hair so you won't need 2nd session. Or if you'll lose it completely (not transplanted one but your own) you'll do 2nd session to close up the left part of it. Or you can wait till 40's and wait for hairs fall out (maybe it even won't) and do a session (or maybe two if necessary) then.