It was an enjoyable enough premiere. Lots more humor than in the past but not anything knee-slappingly over the top.
The main plot of Burnham and Spock's relationship is cringey if only because it seems vaguely incestuous at this point. The mystery of the red dots is intriguing as an overarching narrative for the season. Tig Notaro was great and hopefully becomes the new head of Engineering. Stamets's decision to leave seems very natural given everything he has been through but we all know he will end up staying since he's a series regular -- luckily we have a new science mystery to dig into.
White male science dumbass was predictably a redshirt despite wearing science blue. Women seem to be the only ones with good ideas on the show as epitomized by Burnham. Tilly, also, is a source of ideas as the Ensign seems to be the only person on the ship with a damn brain half the time.
No sign of the Klingon regulars or Emperor Georgiou but we know they will be part of the show even though they weren't in the main credits as they feature prominently in the 'this season' montage.
Overall I had fun with the episode although the extended Pod Racing scene in the second act was a bit superfluous.