I have heard that the "Diving Officer" position on U.S. Submarines can be held by a non-com
...And some Trek bridge positions featured noncoms every now and then even when commissioned officers were more often seen there. I guess the mystery here is the specific reason why O'Brien, apparently a Petty Officer of some junior sort, was selected for the position aboard the Rutledge
, a ship that AFAWK wasn't really, really small and would have had commissioned officers available for the post. And whether becoming "the" TO meant he became one of three or four (one per shift) for some significant length of time, or just was allowed to stand at the console for a week as a reward for saving Captain Maxwell's life, or what.
Mind you, the Rutledge might
have been a midget starship. Backstage sources associate her with the class of the frigate Renegade
from "Conspiracy", namely New Orleans
class. Yet this class was never explicitly, canonically identified with the big starship Kyushu
we saw in "Best of Both Worlds" - so we could take just half of the backstage talk and decide that yes, the Rutledge
was a "frigate" just like the Renegade
was said to be, but no, "frigate" isn't a big ship in the Trek reality, but rather a midget vessel. Which might be why the very junior Tryla Scott was allowed to captain one of those.