No, that’s not a typo — technically, the U.S. declared independence on July 2, 1776, not July 4. As John Adams wrote to his wife the next day, July 3:
The Second Day of July 1776, will be the most memorable Epocha, in the History of America.- I am apt to believe that it will be celebrated, by succeeding Generations, as the great anniversary Festival. It ought to be commemorated, as the Day of Deliverance by Solemn Acts of Devotion to God Almighty. It ought to be solemnized with Pomp and Parade, with Shews, Games, Sports, Guns, Bells, Bonfire and Illuminations from one End of this Continent to the other from this Time forward forever more.
So why do we celebrate on July 4?
Because that’s the day the text of the formal declaration was approved. And when the Declaration of Independence was printed and distributed with the date the text was approved printed at the top, that’s the date that became remembered and celebrated.
The detailed timeline is here. Another thing people often forget is who got the whole thing started:
On June 7, 1776, Richard Henry Lee, delegate from Virginia at the Second Continental Congress, moved “certain resolutions respecting independency” which he submitted in accordance with his instructions from the Virginia Convention. John Adams is generally understood to have seconded the motion, precise records of which do not appear in the Journal.
In this sense, Richard Henry Lee ought to be known as the “father of his country.”