Anyone go through JET and later apply for a Master’s program in Japan?

I’m currently on the JET Program (first year) and curious if anyone here has gone on to pursue a Master’s degree in Japan afterward. How did you go about applying? From my understanding, Japanese universities often require an entrance exam or interview for graduate programs…?Was the process difficult as a former JET? Did you apply while still in JET or after finishing your contract?

Also my Japanese level is pretty low right now, but I’m studying. Do you think it’s realistic to reach around N3 level in 3 years while working in the JET program? I’m pretty much working from the ground up, I’m planning to take N4 test next summer but I’m not even N5 level yet. Didn’t have the courage to sign up for the N5 test this winter. But I think I’ll be ready for N4 by next summer.