Instead of looking at "The Cage", maybe you can look at "Where No Man Has Gone Before" to include some familiar ideas. Instead of Boyce, use Dr. Piper. You can include Sulu, but as an Ensign fresh out of the Academy and assigned to astrosciences.
Personally, I kind of hope for an All Of The Above approach: some characters from The Cage mixed with Where No Man Has Gone Before, sprinkled with some Short Trek characters and background characters from the Such Sweet Sorrow Disco season 2 two-part finale.
Heck, maybe even use some Kelvin timeline characters like Dr. Puri or Helmsmen McKenna (and many others). I know the IDW Kelvin timeline Ongoing and Boldly Go series was hit-and-miss, but I thought it was kind of cool how some of the background characters were built on and utilized in some of those stories. Since the Kelvin timeline voyages and the SNW voyages are roughly set around the same time, I think the two timelines would have more things in common than Spock and the name of the ship.
And of course, add on some new, original characters.
Yes! More Rosa Salazar! Do it! Make it so! Thrusters on full!