its all down to how bad you want it and whose training you. In the uk amatures can box every week if the can get the fights and dont get stopped. If you got the time and a good trainer why not
It is not impossible just not very likely, most top pro's have boxed from a young age and have shown a natural talent. Also your already passed the age to be the youngest world champ in about every division and i don't know of any fighters that started late and went on to be all time greats. Anybody with the heart can be a pro boxer but there is a difference between being good and being a can/punchbag.