I think it is crucial to play a low C without any muscle engagement to release the air. You should be able to take a “concert hall” breath and relax into the C. As you described, this can be quite loud.
Controlling the amount of air that is released could be practiced without the horn. Form the embouchure, as Greg describes, focus on releasing a focused stream of air. Do not push the air. Exhale the air somewhat like a sigh. Do this again, but maintain your posture and keep your chest up. Do not tense any muscles. Keep your shoulders relaxed, but maintain your posture.
I would begin relaxed and loud and then back off on the air. The note should get softer. You will feel the lips close down the aperture, not by you pinching the lips. When playing loudly, the air creates a larger aperture. This is letting lips behave like the vocal cords while singing.
You can sing softly or loudly on a low note without manipulating muscles to force exhalation. It is the same principle in playing a wind instrument.
If you have just recently started this course, don’t rush the process. Practice forming the embouchure and release the air into a tissue (do not blow the air, release the air). Try releasing less air using the tissue and the visualizer or mouthpiece. I was already in the Allegro Stage and found I needed to go back to the beginning.