Social security number for alternance (non-EU student)

I am a new student which will start my studies on 1st September in a private university in Paris. The university offers a possibility to do alternance with a company, a possibility which I used and found a company to work for. Everything was going smoothly until my university asked me for a social security number in order to declare the alternance contract. They got also in contact at first with the company to find a way to get a social security number. The situation seems now a bit complicated because the company has its own rules and cannot issue a temporary number, while the university is quite slow in replying. I am found in a situation where the only hope is getting this NIA from assurance maladie. I have already submitted my dossier and all documents are validated. What worries me is that there is a rule about the NIA (provisional social security number), that I can only get it when the university starts so 1st September. The problem is that my company is expecting to close the procedures before 1st September since that is the day agreed (from university and company) for the alternance contract to start. My final question is: Does there exist any way to get the NIA before the university starts officially or not? Can there not be any exception in such difficult cases? Please help as I feel I am in a never-ending loop and it is not even my fault.