What would your response be to a child who said something similar when you drew a cube?

It does take practise to be able to visualise 4d objects, and I agree that 2d projection example isn't helpful. I find it interesting to think of the 3d -> 2d problem that some people have, and extend it to 4d.

I mean that there is no description on how these projections are even created.

A child would recognize a cube since we naturally see 2d projections of 3d objects as it is. Likewise a 2 dimensional being could recognize a 1d projection of a 2d object (looking at the 2d object on it's side.) But would a 3d object projected to 1 dimension make any sense?