Cold air to the bottom of the mouthpiece, made easier by raising the back of the tongue. Firm up the corners of the lips, avoid saying "more pressure" (even though they may do it naturally which isn't as big of a deal some people make it). I have a checklist that helps them remember how to set their face for low sounds vs high sounds.
If you try all this and it's still not happening, check the horn angle, they may need to angle downward a little more (which again isn't as big of a deal as other people make it.)
Playing a C instead of a G isn't a huge issue, but they should be able to play E pretty well. I used to start on E after a week or two of buzzing bootcamp. Lots of pitch matching on the mouthpiece will help too!