I was doing the asylum challenge, and my sane sim wanted the adventurer career. Took eight days, but luckily she finally got it.
I had a family sims wait 22 days for an opening in the law enforcement track. After about a week I got her a job in the military while she waited patiently for som poor cop to be killed in duty or something. She was an astronaut by the time she finally managed to land a gig as a security guard.
I use harder jobs, and the college job fix thingy, but neither of them should affect this case.