Burnham mentioned this in the very first episode.
You know Burnham isn't the first star trek character to excel in multiple fields or be good at everything right? Let's use Picard for example.
- Was the youngest ever to win the Starfleet decathlon
- Was touted by Richard Galen, to be the greatest archaeologist of his generation, had he not gone into starfleet.
- became a captain in his thirties
- has a tactical maneuver named after him, which is studied at the academy
- considered one of starfleet's best diplomats
- attractive younger women were always into him
- Of all the billions of humans, he was the one to garner the attention of a omnipotent being to challenge.
But yeah burnham = mary sue or whatever