Hi there,
I don't mind starting a new game repeatedly to reroll the random events, but there doesn't seem to be a way to check which random events are active in a particular save. A couple of them have hints, like the dead body in the medical area or the emails about the arena, but the Jet Eater one doesn't seem to have an early game tell. Which means I would have to put in a good number of hours before even reaching core city just to see if the quest has spawned or not. Mostly I'm concerned about missing out on a good boss battle with the Jet Eater.