I don't understand why someone with a degree wouldn't get a commission instead, but it's your character to make that choice for. Nothing strikes me as wrong or inappropriate.
Approved for the plot.
Feel free to post in the thread. Your character hasn't been briefed about the situation other than the commonly-known facts of Kuvexia's invasion plus having been told that the ship she's assigned to is immediately deploying on a SAINT mission behind enemy lines.