My classes started on the first week of October and my flight was on September 12th. It might sound early but I had two weeks of orientation, then on the third week I had to do health checkups (again), make the health insurance registration, open a bank account and so on. It's actually quite a hurry. It depends on the university, but prepare to fly around two to three weeks before your classes start. There were people who left a week earlier than me (and their classes started on the same day as mine), and there were those who went almost a month later (because their classes started later). I only knew the day of my flight around one month before the departure, which means that, until my classes started, I was just running around to hand in all the documents in time, in my home country and in Japan.
Also, the university is responsible for you, so I don't think they would just leave you with nowhere to live when you arrive, but you should talk to them about it before going.