Applying for a job in Japan

Hey guys heres my situation, I am about to graduate in april with a bachelors degree in Asian Studies ( Language Concentration) and would really like to come work in Japan and ultimately live there one day. My question is in regards to getting a job as an ALT, I just recently found about JET because my school isn't helpful at all and the deadline has passed : ( but i looked online and there are other companies that do the same thing : )! My question is how soon should i start applying to the jobs because i don't want to wait until after i graduate and have the process take months and meanwhile Im out of a job.

Please any advice will be most welcome and thank you so much in advance. I am an american citizen btw i don't know if that changes anything.

I think 6 months before you graduate would be good. It'll show them your enthusiasm and your seriousness. Good luck.