I’m a new sax player and my teacher recommends I play the mouthpiece
and head for two weeks. Is that necessary to start playing?
That would make you focus on one thing, which is trying to get a better tone and playing around with control. That is something you really should do, but it becomes easy to shift your attention to your fingers once you have the whole saxophone and then the tone may get overlooked for a while.
Once your fingers are involved, they are directly linked to your sound. So how you move your fingers can cause problems with your tone.
If your fingers aren’t involved at first, your tone is controlled by your breath and embouchure which are two important elements of playing saxophone.
Doing what your teacher recommends also may help show you the importance of focusing on one thing at a time while learning to play.