Was doing a transit directions/trip planner in Google Maps when I saw this option pop up, apparently launched last Sunday.
SamTrans Launches ECR Rapid, Route SFO
Route info and timetable:
Route SFO
FREE RIDE Promotion!
Try the service for FREE between June 24 and July 7. After the free promotion, regular fares apply. Farebox accepts cash only fare: $2.25 for adults, $1.10 for Seniors and Youth. Riders can also pay with Clipper Card for a larger discount! See FARES for more info.
Route SFO will run direct service from the Millbrae Transit Center (Caltrain and BART) to terminal stops at San Francisco International Airport including International Courtyard A, Terminal 2, Terminal 3 and International Courtyard G. All buses will have additional luggage racks.
FlySFO.com:
https://www.flysfo.com/to-from/public-transit
SamTrans Route SFO connects each Airport terminal with Caltrain's Millbrae Station. It is timed to meet each Caltrain service to and from the south, 7 days per week.