So I am going to Tijuana tomorrow in the morning, I cannot find my birth cirtificate however I have a California issued ID along with my SS card, is it possible to cross in and out with both documents?

Show id state your citizenship I Always Pass You Will Not Get Detained

Of course you will be able to cross. Even with out an identification card. You can not ever be denied entrance to the US if you are American citizen. Finger print you. No worries you will be fine

Yes

They can detain u or fine you as well but should let u back in

Be aware that if you take the pedestrian crossing into México they now frequently check for a passport and require you to pay for a travel visa (7 or 180 day variants). I do not believe they will issue said visa without a valid passport. Curiously I have never been checked for a valid passport while travelling south in a vehicle lane, though.