Unfortunately Chinese Immigration will only accept the actual graduate diploma/certificate. (They won’t accept letters or transcripts or really anything else).
It is fine to start on the other paperwork but getting the diploma authenticated for the work permit process is one of the most time consuming tasks (see other notes on the authentication process)
It is best to put more pressure on your university to give the actual diploma, ask if you can go and pick it up, and explain clearly to them that you have a position but Immigration will not accept anything other than that document.
Often MEF is able to work with delays and still get you working regardless, but try your best to get that needed document quickly from your university.