After the collapse of British authority in 1775 it became necessary to form new state governments and by the end of 1777 ten new state constitutions had been created. Connecticut and Rhode Island kept their colonial charters but removed all references to British sovereignty. Massachusetts waited until 1780 to adopt it's new Constitution. All of this prior to adoption to the Articles of Confederation!
The were already free and independent states prior to their becoming party to any union whatever!
The Treaty of Paris acknowledged the 13 colonies to be free, sovereign, and independent states and that the British Crown and all heirs and successors relinquished claims to the Government, propriety, and territorial rights of the same, and every part thereof.
The Treaty of Paris was an agreement between King George and the United States of America, not 13 seperate, sovereign entities. It was proclaimed between the U.S. and Great Britain and was signed by John Adams, Ben Franklin, and John Jay on behalf of the U.S.