Kids don't have to watch from the fence in San Francisco Bay Area: 2 local tracks have evidence of junior karts, family sessions or young drivers on track — not just arcade games in the lobby.
Height matters more than age at most tracks — junior karts typically need drivers around 40–48 inches tall, and requirements differ venue to venue. Check the track's page below for specifics, and confirm with the venue before you drive out.
K1 Speed South San Francisco, K1 Speed Santa Clara — all listed below with ratings and contact details.
Go Karting USA lists 2 operating tracks around San Francisco Bay Area — see the full San Francisco Bay Area guide for all of them, not just kids go-karting venues.