In California can the DMV make it possible for a 16-year-old to drive alone to school with only a driver's permit?

There is no way! The only way to drive alone is on a provisional license which requires 6 months on a permit, 3 drivers training classes, and the Drivers ED.

Actually yes you can. If you go to the dmv's site, there will be an exceptions section where you can go to school by yourself as long as the prinicpal signs a note or document stating that you may do so.

Technically, the DMV does not have lawmaking authority so it is not up to the DMV to determine who can drive when and under what circumstances. This function is left to the state legislature. The legislature could make it possible for a 16-year-old to drive alone to school with only a driver's permit if they were so inclined, though I doubt they will be so inclined any time soon. And with reference to the answer posted above, it appears to have confused exemptions to the first-year-license restrictions as exmptions to restrictions of drivers permits. A fairly exhaustive search of the CA DMV website uncovered NO exceptions to the requirement that a learner's permit holder must have a certified driving instructor, a license-holding parent/guardian, or other license-holding person aged 25 or older in the car with them while driving.

To the person who said..

[There is no way! The only way to drive alone is on a provisional license which requires 6 months on a permit, 3 drivers training classes, and the Drivers ED.]

You can get a permit at 15 and a half, if you need 6 months with a permit, you can get a permit at 15 and a half and when 6 months pass by, you're 16.