I love the show, but I do kinda think the determination to make this a "below decks" show was a failed experiment. Here we are, focusing on the captain, wondering if and when will the lead become the captain, and wondering where the CMO is. It might just be in the DNA of Star Trek for the leads to be the command crew.
Yeah, it's really jarring if you look at Episode 3, where Tilly was just a lowly tech under Stamets who happened to be Burnham's roomie. She started out being integral to the story because she was as close to a friend as Burnham was going to get, but now she gets to be integral to resolving all of the issues just because they need to give her something to do.