As @ReneeM7122 advised, wait until the IRS issues an ITIN and then file the CA state tax return.
2020 Instructions for Form 540 does not provide a method for filing a joint tax return when one of the joint filers does not have a SSN or ITIN. There are provisions for including a dependent with no SSN or ITIN (FTB Form 3568), but not a joint filer.
