How did Zander Barcalow get to be an instructor so quickly?

Remember first, Zander went into the Service well before (months) before Carmen, Carl, and Rico joined up. During this time he has already gone through flight school and is established as a pilot on the ship. In order to attain this position (pilot), they need to be the best and the brightest ... extremely good with math and such. When Carmen arrives on the ship, she has just made it through flight school. At this point, Zander is not her instructor, but rather her mentor. She is qualified to fly the ship as she has already passed through flight school. BUT, there is practical learning which they did in school, and now a brand new pilot needs someone to show them the ropes in the real world. It isn't that Zander has risen so fast, it's that he's qualified to pilot the ship, so is qualified to mentor Carmen in the process.

According to the film script it's actually Captain Deladier who is the Instructor. Zander is merely Ibanez' supervisor and a lowly second Lieutenant to boot, a rank that Ibanez evidently secures as soon as she qualifies as a pilot, a few weeks later:

ATHENA - COMMAND AND CONTROL - DAY CYCLE - CARMEN arrives on the bridge, dark, cramped, all-business. She salutes the instructor, CAPTAIN DELADIER, 40s.

CARMEN: Pilot Trainee Ibanez reporting for duty, ma'am.

DELADIER: Take the number one chair, Ibanez. Follow all instructions of you supervisor.

CARMEN: Yes, ma'am!

Carmen turns for her station, but stops in her tracks. Her supervisor is Zander Barcalow, now a 2nd Lieutenant.

Since Zander was already shipping out when they were finishing high school, it's certainly possible that he attained his rank in much the same timescale without the need to construct elaborate theories about him already being at Flight School but for some reason still playing High School football.