Mage-Specific House Rules/Buying Spheres
Mage 20 implies that a mage has to have a teacher of the same focus to raise spheres, i.e. someone from your Tradition, Convention or sect. However, this is supposed to happen during downtime on a tabletop campaign, and we are a 24/7 campaign. Thus, it's simply not effective and will lead to headaches.
So, yes, you can learn spheres without a teacher.
However, to reproduce the complexity of learning them you can only learn one sphere per RL month. So choose wisely.