You may not know that July 4 is not the birthday of the United States of America. The Declaration proclaims that the colonies are “free and independent states;” it does not say that they are united as a single independent country. That is undoubtedly why Jefferson did not base the argument for independence on the emergence of a new American nation separate from Britain, as one undoubtedly would do today, and Hamilton probably would have done even then.
The Declaration could have been the precursor to an “America” that was just a temporary military alliance of the states, or even less. The legal reality of the “United States of America” was first articulated in the Articles of Confederation. Without the Articles, each of the individual states would have been required to sign the Treaty of Paris as a separate combatant in 1783, which would have been absurd.
If you want to celebrate the birth of our nation, you will consequently have to wait until November. If you are satisfied with just celebrating the break with Great Britain, have a great July 4!