The company hasn't paid me social security for two and a half years. What should I do if I report him and ask him to compensate me? Specifically, if I sue him, what is the process?

You can sue him with the contract you signed, because it is illegal not to provide insurance after the application period. The best result is that the unit will make up the insurance owed to you, and the possibility of compensation is not great.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.