Since General George Custer was still alive in the movie, it was earlier than 1876. But two songs sung were composed in 1900 and 1933.
George Custer was not a General. He only held the temporary rank of Major General during the Civil War. After the war he reverted to his permanent rank of Captain. He was appointed to the rank of Lieutenant Colonel when dispatched to the West. Lieutenant Colonel was the highest rank he obtained before his death.
Lee Bowman's character is continuously referred to as Lt. Connelly and wears officer's bars on his uniform, yet is listed in the credits as Sgt. Connelly.