So based on my very limited experience:
I made the move from starter (2.3" jumps and BN Dressage) to BN at the beginning of the year because I knew that we could get through starter without any issues. Our practice (jumping 2’6" - 2’9" courses at home) led me to believe that we wouldn’t have any issues with the jumping portion of BN. I fixed up our Dressage work went XC schooling once and went out to an easy BN schooling HT.
Overall, we got a 30.3 on Dressage, one rail in SJ, and a refusal at the water because we forgot how to steer. I think sometimes people are afraid of having “green” moments at horse shows, but it rarely gets better if you don’t get that experience.
The move up to Novice won’t happen until our Dressage takes another step forward, we lose the greenness over Stadium, and we have answered all the Novice level XC questions successfully in schooling.
TL/DR: If you and your horse can comfortably approach all the questions asked at the level you want to move to, it is most-likely a good time to move up.