The Japan's fast-track system you mentioned is called highly skilled foreign professionals. To obtain the highly skilled foreign professionals, there is a scoring system. If your score is over 70 , you can apply for this. If you can obtain this kind of residency you can get permanent residency quickly (under certain conditions you can get permanent residency in a minimum of one year).
What can make my permanent residency application better under Japan’s fast-track system for resident visas?
I heard about the point system for skilled foreigners in fields like academic research or business management. I have considerable business experience but am not sure I would qualify. What levels of experience is Japan looking for that can boost my application to live there?
You need to have a contract with an organization in Japan to receive a certain amount of remuneration for your work. If you reach 80 points, you can apply for PR status one year later.