Some sites put her as 3rd, some as 4th behind Sulu. The important part is that she was an FU to the network. They said “you can’t have a woman (white in this case) be 2nd” and he stuck an alien (which they also wanted to get rid of) in 2nd, a black woman in 3rd or 4th, and a Japanese guy in 3rd or 4th. He deliberately went more diverse for the 2nd pilot.
Scott was 3rd. She was probably 4th. Didn’t they call her Lt. Commander? Or was that in the movies?