…but we’re trying to set the air in the trumpet vibrating.
That’s why we don’t need to push/blow into the trumpet, we just need to strike the air column enough to start it vibrating, and then maintain the vibration for as long as we want.
Pushing/blowing into the trumpet is like trying to play drums by smashing the drumstick all the way through the drum. Rather, we just need to strike the drum skin just right to set it vibrating.