You may be wondering at the title, since most have always been taught that July 4th is Independence Day.
On July 2, 1776, the Continential Congress adopted the resolution of Richard Henry Lee to declare the American colonies independent of Great Britain. The vote was unanimous, except for New York, which abstained.
The (edited) version of Jefferson's historic Declaration of Independence was adopted two days later, on July 4, 1776. But the version of the Declaration that was adopted was actually signed on August 2, 1776.
So, if you want to go according to the first official act of the American colonies to declare themselves "free and independent states", you would go by July 2, 1776, the date the United States of America came into being.
Happy Birthday America.