At the Treaty of Paris, September 3, 1783
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The Declaration of Independence was the written separation from England by the Thirteen Colonies. It basically stated that England no longer had control over the colonies, and was signed by the representatives of the Thirteen Colonies.
the first foreign port to acknowledge the independence of the 13 colonies is the port of Spain
It's the Declaration of Independence. The thirteen colonies declared their independence from Great Britain.
By mutual consent all thirteen had to vote in favor of independence. That's why the formal document (the "Declaration of Independence") specifically points out that this is a unanimous declaration.(This does not mean every single individual in Congress, but that each colony's/state's delegation would vote, and a majority of "no's" in any delegation would defeat the measure.)
As to the question of whether the 13 colonies could have declared independence if they weren't unanimous, answers will vary. Most might state that independence would be difficult without the support of all thirteen colonies, but some might say independence without consensus was still possible. For instance, colonies that objected could be absorbed into Canada or find a way to peacefully co-exist with those that seceded.