While it is true that the office of the President of the United States took on a radically different meaning under the new Constitution in 1787, the Nation did de facto exist, as evidenced, for example, by Treaties which the United States, as a Sovereign nation, negotiated with other sovereign nations during the time period between 1776-1787.
Under the Articles of Confederation, even thought they were insufficient and eventually replaced, there was an office of President, and, if I'm not mistaken, it was actually John Hanson who developed the Seal of the President of the United States which is used to this day.