He can certainly be an AE. I hope you don’t feel I was suggesting otherwise. He can’t however just move into a graduate program in AE without a major backfill in his education. As a CS he’d probably need to step back all the way to second year engineering classes, certainly dynamics, if not statics. If he’s interested in SpaceX (he should talk to friends there to really find out; it’s known as a tough place to work), why not work as a CS?
As for the challenges of getting a job even for the best papered, I can relate! My son (BS Magna Cum Laude MS With Distinction, ME) was particular, but he applied to a bunch of positions and heard crickets. He was hired as the first new grad to an elite team of industry veterans at a hot startup. They obviously saw something in him that those hiring for the “shoe in” jobs didn’t. There’s no rhyme or reason, other than people hiring are looking for experience. He’s been headhunted since.
Best of luck to him!