The signers of the Declaration of Independence weren’t setting up any government at all. They were declaring that the colonies, the predecessors of our present day States, were henceforth independent of England.
Later, these same States relinquished SOME of their powers to the newly created Federal Government. But, the vehicle by which THAT was accomplished was NOT the Declaration of Independence. Not by YEARS.
The Constitution and the Declaration of Independence are two DIFFERENT documents with differing significance for our history and for our jurisprudence.
It is impossible to rightly understand the Constitution apart from the Declaration. The Declaration is the spirit of the Constitution.