Presumably with a rapidly opening door. Of course now you have to design your rocket to slam into an atmosphere at launch velocity.

You might have to install enormous compressed air tanks at the end to pre-accelerate the air right as the door opens just to make it less like hitting a brick wall of onrushing air.

Can't you do something similar to what the engineers in the rocket throwing video are doing?

By extending the cannon's end to space.

A door.