In my experience, I have met medical assistants who have been promoted to the level of lead supervisor or who have transitioned into positions in medical office management. In the same way, I have also seen medical assistants at my job who have pursued education in other healthcare areas such as nursing school, or pursued education in other fields related to healthcare. Healthcare offers many opportunities!
Over the years I have worked in medical offices where the office manager started off as a medical assistant and worked themselves up to being an office manager. This was in the days where there were more privately owned practices; but I doubt in today's work environment that would be a possibility without earning your higher educations (college degree).