By act of the Continental Congress the United States Navy was created on October 13, 1775 in Philadelphia.

It would be safe to assume that the place of creation for the United States Navy was Philadelphia in conjunction with the resolution which ordered the building of a naval fleet. That assumption could be correct. That assumption could also be incorrect.
The answer is it depends…
Even the U.S. Navy itself is unwilling to take a firm position on the topic.
Philadelphia, Pennsylvania
Philadelphia has a strong claim to the military fame. The resolution ordering the creation of the United States Navy was issued in Philadelphia.
Machias, Maine
For early naval exploits Machias, Maine takes the prize when the British Navy schooner Maragretta
In Massachusetts, both Beverly and Marblehead claim fame
George Washington authorized the ship Hannah to harass the British fleet from Beverly and it was owned and manned by residents of Marblehead leading both towns to claim the title.
Providence, Rhode Island
Providence stakes a claim to the birth place of the Navy by virtue of the fact that the state’s delegates were the first to call for the establishment of a Navy.
Whitehall, New York
Whitehall also claims a part in the birth of the United States Navy. Benedict Arnold used ships built in Whitehall, New York to harass British interests on Lake Champlain.
The Navy had many birthplaces
The birthplace of the Navy is one of the questions of history that may never have a settled answer. The United States Navy probably takes the safest answer with the explanation that the Navy has many birthplaces.
Where is the birth place of the Navy? That question has been asked many times since the creation of the force in 1775 and it does not seem to be one of settled debate in the future.
Five different states and six different cities. The birthplace of the United States Navy is a source of heated debate as old as the Navy itself.
Happy Birthday United States Navy
Sources:
Naval History and Heritage -Birthplace of the U.S. Navy
National Archives Pieces of History – Where was the Navy Born?