Good day! Can I obtain Z visa when on a tourist L type?

I am planning to go to Shanghai on a tourist L type for 3 months to look for a teaching position in person, visit the schools etc. I am concerned that I perhaps can't obtain a Z type and the other permits etc to teach and work in PRC when in Shanghai on a tourist L type. Will I need to fly back to my home country first before I can obtain my Z type? Or can I do the process of the Z type all while staying in Shanghai without exit? Thank you!