Leaving the country while getting a residence permit

Here, you are suggested to submit your application for residence permit asap after you enter China, it takes 5-7 working days to finish the health certificate through a local appointed hospital and 5 working days to go through the registration procedures for the Residence permit at the public security bureau. The residence permit works as a multiple entry visa. So, you can try to tell the officers that you need it in shorter time and they may consider your situation, or they can extend your visa for another entry. BTW, it is better if anyone in charge from your university can go with you when apply for this.