The Clipper program in the San Francisco Bay Area primarily has senior/youth discount cards issued primarily through mail, online, or FAX applications. They'll require a scan/image/photocopy of proof of age. This says 5-18, but I obtained my child's card before turning 5 (when any fare requirement started for any covered agency), where it was set up to automatically apply any youth fare based on DOB.
https://www.clippercard.com/ClipperWeb/discounts.html
But there are some locations that can issue such cards in person. Some locations (like senior centers) are limited to specific types. I obtained my child's youth Clipper card when I was working near the Santa Clara Valley Transportation Authority headquarters. I had to search around the building but found it. I brought my child's California ID with DOB as proof of age. A designated employee had to be called in and then I had to wait a few minutes for him to come back with a card. One would need to enter a location and select "Staffed Location" from this dropdown menu.
Staffed locations
Buy an adult Clipper card, get a Youth or Senior Clipper card or load value on any card. Call ahead for days and hours. Card replacement services available at
select locations.
San Francisco gets a lot of tourists, so a primarily location would probably be at the Ferry Building or near a Cable Car turnaround. The first one on this list is near the Market/Powell Cable Car turnaround and I think their biggest business is selling Cable Car tickets.
SFMTA Powell and Market Public Transit Kiosk
899 Market Street
San Francisco, CA 94103
Phone: 415.701.2311
SFMTA Presidio Sales Kiosk
949 Presidio Street
San Francisco, CA 94101
Phone: 415.701.2311
Clipper Customer Service Center at Embarcadero BART/Muni Station
298 Market Street
San Francisco, CA 94105
Clipper Customer Service Center at Bay Crossings
1 San Francisco Ferry Building
San Francisco, CA 94111