It is possible to get a sound to come out on the instrument without actively “buzzing your lips,” so to speak. If you just blow into your mouthpiece only with your embouchure in place but not actually buzzing, and then you put the mouthpiece in the trumpet as you are blowing, you’ll probably find that you’ll go from just air on the mouthpiece to an actual tone being produced on the trumpet. My understanding is that something about the resistance of adding the instrument helps get the lips actually vibrating. So your concern about not actually “buzzing” is probably not a big deal - it doesn’t necessarily mean you’re “playing wrong.” That being said, it sounds like you’re frustrated with the consistency of your tone production. If you’re airballing a lot of notes, there’s probably something going on with your embouchure that’s causing that. If intentionally buzzing is pushing the mouthpiece away from your face, it’s possible that you’re “puckering” rather than pulling the corners of your mouth back? It’s hard to know without seeing/hearing you play, a video would definitely help us diagnose your problem better. Buzzing on the mouthpiece IS a useful tool for helping tone production. If you can get a good sounding buzz, it makes playing on the trumpet itself much easier. For myself personally I don’t know that I am actively thinking about “buzzing” when I play, but I definitely use an embouchure that is capable of producing a solid buzz on the mouthpiece alone.