You want to start as early as possible. Waiting until the last minute can be detrimental to your medical school applications. Like with medical shadowing, volunteering may require paperwork and formalities that must be completed before you can begin.
Starting early allows you to have time to handle any concerns and gives you a chance to work on projects for a longer period of time. Consider starting in your freshman year of undergraduate school. Some students start as early as high school with activities they continue in college, which is great. If not, strive for your freshman year of college.