Can I apply for a teacher's apartment in Shanghai Jiaotong University without preparation?

You can't. According to the inquiry of official website of Shanghai Jiaotong University, the application condition for teachers' apartment is that Shanghai Jiaotong University officially serves as a teacher, and it cannot be applied without the establishment. Shanghai Jiaotong University, referred to as "Shanghai Jiaotong University", is located in Shanghai. It is a national key university directly under the Ministry of Education, built in Shanghai and directly under the central government.