What month was the first US submarine built?

Though the first American submarine was the Revolutionary War's Turtle, the U.S. Navy did not exist at that time.

The U.S. Navy's first submarine, the USS Alligator, was built in 1862, and active in the Civil War.

The USS Holland (SS-1), was the U.S. Navy's first commissioned submarine, had her keel officially laid down at Electric Boat in November, 1896. She was commissioned in October 1900.