The Declaration of Independence has no legal significance. It is just a letter, and the prose is intended to be poetic (to justify violent revolution) rather than functional.

Your comment about the U.S. not existing shows a misunderstanding of the nature of the Constitution. The Constitution is essentially a contract outlining the delegation of powers to the federal government from the sovereign state governments. The rights therein were viewed as already operative, but not because they were viewed as rights intrinsic to humanity, but because they were rights already enjoyed by citizens of the several states. When the Constitution talks about "people" it is not talking about "people in general." It is talking about "the people"--the body politic of the several states which combined to form the union. Those are the people who have rights under the Constitution.