The Constitutional Convention in 1787 of the now independent States, after months of debate and disagreement, the majority delegates finally agreed with the newly written Constitution in September 1787. That would be the informal origin of the United States of America. The formal origin is when holdout States ratified the Constitution in 1789.
I thank you for all you have done to further our Constitutional Republic. Bless you.
The second to the last sentence says so (it is long though, for a sentence)...
We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do.
By independent they also meant united--small u. But all together fighting as one nation, with one military, one peace, one alliance, one commerce, etc., shared together and not 13 separate ones.