[El Gato]

But the United States of America was not formed until September of 1787, with the ratification of the U.S. Constitution.

The Constitution was passed by the Convention in September of 1787, but was not ratified by the required 9 states until June 21, 1788, when New Hampshire ratified it. Followed in 4 days by Virginia and in just over a month by New York. NC and RI were holdouts until Nov. 1789 and May 1790 respectively.

But, the United States Of America, by that name, came into existance in March 1781 when the Articles of Confederation were ratified. (They had been sent out to the states in 1777, but there was other pressing business, plus a few state's legislatures were in hiding, or operating far from their normal venues. From the AofC:

Article I.The Stile of this confederacy shall be "The United States of America".

Although one could argue that the United States came into existence on July 4, 1776, with the passage "in Congress assembled" of the Declaration of Independence, since that document was subtitled "The Unanimous Declaration of the Thirteen United States of America"

[K-oneTexas]

Historically correct. But there was something specific the Founding Fathers wanted to say and thus: "No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, ... " I'd say they were pretty specific and historical factt did not matter in this case.