How long does it take to become proficient?
This depends on the definition of proficient. If you practice diligently and have a good teacher, you should be able to play simple songs within 8 weeks. If you want to become a virtuoso, this may take years. There is nothing inherently easy or hard about the accordion, much like all instruments. (There are really no easy instruments nor are there any that are inhumanly more difficult than others!) But it does take time to master the skills of musicianship so that you play acceptably for yourself and others. First, please yourself, then your family, next your friends and finally your public.
So in short, with focus, you should begin to sound okay in a few months. Within a year, you'll have some good mastery of basic songs and techniques. In five years, you should be a whiz. The old saying "How do you get to Carnegie Hall?" is answered with "Practice, practice, practice." There's no magic bullet and no easy route. The earlier you begin in life, the easier it is to assemble the skills. Nonetheless, older folks can bring themselves to a good level of mastery with practice and focus.
Playing music for yourself and others is a joy, even though the road to mastery is not easy. Good playing always looks effortless, even if you are putting your entire mental and physical being into the process.