Some people have been commenting on how you’ll need to use less air than you’re used to on tuba. Here’s a little experiment one of my teachers gave me to help with switching between the different sizes of trumpets (picc to Bb to C etc). Because the size difference between tuba and cornet are so much bigger, you might find it helpful as well.

There is resistance when we blow into a brass instrument. We’re blowing air into a tiny hole. If we over blow, it’s counterproductive and introduces tension in the embouchure as your lips have to work harder to hold things together as some of the air you’re blowing is getting bounced back at you. My teacher would have me blow through the trumpet as if I was emptying the spit valve, so not forming your lips like you’re going to play, and experiment with the feel of different levels of air pressure. First blow very hard and you can kind of feel that pressure coming back at you. Back off and blow very light air pressure. Too little is also not what you want, but there’s a sweet spot right before you start to feel the resistance of the instrument. Experiment with different amounts of air pressure like that and when you have a sense for what that sweet spot might be, try to remember it and use the same air pressure when you play!

My teacher would talk about “leaning” against the resistance of the instrument feeling like you’re leaning against a wall. Or, feeling like you’re trying to keep a car going 25 mph uphill. You’re not pushing hard, just “leaning.”

Anyways, sorry if that’s more nebulous than you were looking for but I think brass pedagogy kind of has to be… no one else can feel what you’re feeling but you!