Can you get Excelsior Pass Plus? D
igital cards initiatives in the US - CA, HI, LA, NY Excelsior Pass Plus, VA, some major chain pharmacies and few hospital systems all issue Smart Health Cards and is tied to CommonHealth and CommonPass. Each digital card can be verified by the Smart Health Verifier app. (The verifier app is extremely buggy and annoying to use but that is a different story). Each of the state/pharmacy chain issued digital card can be saved as a PDF or imported in CommonHealth app or the state's own app. I have no idea if California requires vaccine proof for anything but it should be able to verify a Smart Health card.
For international travel you probably need a CDC card just to be safe. Maybe go back to the site where you got your shots and they will issue a replacement card?