NSNoob's answer addresses the dating of the Declaration of Independence well enough. My answer will touch on why early July 1776 was distinct from the other dates in your post.

The disagreement between colonials and the British had already resulted in shots fired and battles fought in the previous year, such as Lexington in April of 1975, Bunker Hill, the seige of Boston (April 1775 - March 1776), Knox and Arnold's successful raid and artillery haul from Fort Ticonderoga in mid-1775, and so on.

Despite all of this action, it was not yet definite as to whether this was an armed insurrection, a civil war between Britons, or an outright split. Indeed, the thought of colonial independence from the Crown had been generally unthinkable despite the couple decades of disputes, scuffles and high-minded statements made leading up to 1775 (The Glorious Cause: The American Revolution, by Middlekauf). After all, statements of independence was still treason during this period and there was still a close (and yet also distant) relationship between Britain and the colonies during this time.

Political movements and some public sentiment gained traction by 1776 to specifically address how this relationship between Britain and the colonies now stood, and the Declaration of Independence was the result. The Declaration was the Official Notice from the colonies to the Crown that they were now independent. With that statement made, there was little chance of going back without serious repercussions, since the Continental Congress was now liable for high treason.

The later victories during the Revolutionary War defended that notice of July 4, 1776. It took even longer to form the first government and evolve it into the government we generally recognize today. But it was that date when the irrevocable Official Notice was served, and that focused the colonial's desired outcome for the rest of the Revolutionary War.

NSNoob's answer addresses the dating of the Declaration of Independence well enough. My answer will touch on why early July 1776 was distinct from the other dates in your post.

The disagreement between colonials and the British had already resulted in shots fired and battles fought in the previous year, such as Lexington in April of 1775, Bunker Hill, the seige of Boston (April 1775 - March 1776), Knox and Arnold's successful raid and artillery haul from Fort Ticonderoga in mid-1775, and so on.

Despite all of this action, it was not yet definite as to whether this was an armed insurrection, a civil war between Britons, or an outright split. Indeed, the thought of colonial independence from the Crown had been generally unthinkable despite the couple decades of disputes, scuffles and high-minded statements made leading up to 1775 (The Glorious Cause: The American Revolution, by Middlekauf). After all, statements of independence was still treason during this period and there was still a close (and yet also distant) relationship between Britain and the colonies during this time.

Political movements and some public sentiment gained traction by 1776 to specifically address how this relationship between Britain and the colonies now stood, and the Declaration of Independence was the result. The Declaration was the Official Notice from the colonies to the Crown that they were now independent. With that statement made, there was little chance of going back without serious repercussions, since the Continental Congress was now liable for high treason.

The later victories during the Revolutionary War defended that notice of July 4, 1776. It took even longer to form the first government and evolve it into the government we generally recognize today. But it was that date when the irrevocable Official Notice was served, and that focused the colonial's desired outcome for the rest of the Revolutionary War.