Without this letter, it does not appear possible for a visa to be issued. You may have a residence permit, But it can not allow you to enter China. Based on feedback, to get the invite letter issued, you should be working at a company that has demonstrable economic impact in China (based on headcount, revenue, etc).
Note that some Companies and schools in June 2020 first tier cities have successfully arranged PU invitation letters for staff
PU invitation letters are valid for 3 months from date of issue.
The only way to get this PU letter is by factory or agent to apply it in the foreign affair office.