Japan Student Visa to Working Visa

Hi! I’m currently on a Student visa in Japan for 2 years (April 2024 start), and would want to switch to a Work visa as the main objective.

Of course, I understand that I will need a company who’s wiling to sponsor me a working visa. My questions are:

1. When should (or could?) I start job hunting? Can I start applying even before my course completion?
   1.5 Any useful agencies, websites, or support groups (Hello Work?) ? Do you think my school would help me land one?
2. What is the typical timeline/duration in switching visas?
   2.5 When should I time my application/notification for a change of residence status?

I’m assuming it’s all in a work before my student visa expires, though I know, I can switch to a job hunting visa after graduation.

I have a master’s degree and have 5 years if experience in IT project management, if that helps.

Thank you so much for those who would give their suggestions.