That is absolutely untrue, as evidenced by the fact that the former colonies did not all agree on what form of government they would adopt after the Revolution. Vermont was a perfect case in point. It was conspicuously absent among the original Thirteen States because the "American patriots" from Vermont who fought against the British at Ticonderoga and at Quebec -- Ethan Allen and the Green Mountain Boys -- had their own ideas about how they wanted to organize after the British were defeated. The Vermont Republic was established as an independent state in 1777 even before the American Revolution was over, and not long after the Declaration of Independence was signed. Interestingly (and not coincidentally), nobody from Vermont ever signed the Declaration of Independence.
The Declaration of Independence uses the phrase "the united States of America," and the Articles of Confeeration, completed in 1777 (but not ratified by all 13 states until 1781), says that the "style" of this confederacy shall be "the United States of America."
Vermont is an exceptional case because it was territory claimed by two colonies, New Hampshire and New York, and the actual settlers there managed to make themselves independent of both. The delegates to the Second Continental Congress were all from officially recognized colonies--so naturally there was no one there from Vermont, so no one from Vermont signed the Declaration.