The act that institutes the government is not a contract but a law.
Gist of Idea
The government is instituted by a law, not by a contract
Jean-Jacques Rousseau (The Social Contract (tr Cress) , III.18)
This is a law which implements the general will. There is nothing for citizens to make a contract with, since the sovereign is an abstraction, whereas a social contract is made between actual people. I like Rousseau's big idea.
Rousseau,Jean-Jacques: 'The Basic Political Writings', ed/tr. Cress,Donald A. [Hackett 1987], p.202