And I would argue the United States of America existed from the time of the Declaration in 1776.
So would I, but in this case, it doesn't matter. Both President's born after the Declaration, but before the Constitution, were also born after the Articles of Confederation were adopted.
The spirit of the nation began with the Declaration of Independence, I’ll grant you that. But, the legal entity came into being with ratification of the Articles of Confederation by the States. Citizenship is a legal concept, that was in dispute with the former sovereign to greater or lesser degree over the best part of four decades, and it took two wars to settle once and for all.