The star of Star Trek: Discovery has come out and said that her character, first officer Michael Burnham, will eventually captain her own ship. We have a question or two about this.
In an interview with Den of Geek, Sonequa Martin-Green was asked whether she envisions a future where Michael Burnham could become a captain. This seems like an impossibility, considering Burnham was court-martialed and sentenced to life in prison for mutiny against Captain Georgiou, an action that led to Georgiou's death and the war with the Klingons. Martin-Green replied that not only is this something that she personally wants, but that it's part of Burnham's character journey.
I definitely think that's in the future, and that's part of the journey for sure. We're certainly not closed off to it, but who knows when. It's certainly a part of it because that journey to captain has been driving Michael from the very beginning, and definitely since joining Starfleet. That progression and that yearning to ascend is almost a pillar in her personality.
Here's the thing: There's some precedence for this. In Voyager, Tom Paris was taken from a penal colony to help Starfleet and, when the ship was yanked across the galaxy, Captain Janeway made him an ensign and the primary helmsman. And in the expanded universe - canonically grey-area material set after that series - he does eventually make captain.
The circumstances of Voyager and Discovery aren't too different. Except, of course, Voyager is set way in the future of Discovery, when people may have become more lenient. Also, Lorca's captaincy on Discovery is a bit more questionable than Janeway's - Starfleet Command is less likely to take his word than they were Janeway's. And Tom Paris's actions were much less notable than Burnham's, who we're constantly reminded is "Starfleet's first mutineer".
So while it isn't impossible that she'd eventually become a captain, it feels a LONG way off. Longer than this show has, probably.