M.K.
In order to change the birth certificate I would go directly in person to whatever office with CA Health Department. Don't even try to do this over the phone or through the mail. You might need to take a day off work but that might do the trick. Take every paper you might need and identification. Once you get that sorted out you should have no problem with the passport. When my baby was born we needed a passport right away so my husband hand carried all the paperwork to the records department and got the birth cerificate, SS card and put in the paperwork for the passport all in one day. In today's world there is no reason this should take 5 months, everything is computerized and all it takes is one person to correct the error and print it out. Good luck!