If I hadn't quit my last job, But my last job company didn't pay me social security. I am now in a new company. Does it matter if I have to pay social insurance?

Maybe, your company didn't pay you social security before, so they violated the rules. But did they help you join the job, that is, they went to the labor agency to help you with the recruitment record. If they do, your file will be in the name of this company. If they don't help you resign, your new company will not be able to help you complete the new recruitment documents. Without the recruitment record, your file will not be transferred and you will not be able to pay social security.