In my husband's case with his oldest daughter, he was willing to sign the birth certificate, but his ex would not declare him the father. She also stated that there where two possible fathers to DSHS (she was on welfare and they have to try to figure out who the father is), so I believe that DSHS paid those costs. After it was confirmed that my husband was the father he had to pay DSHS back some of the hospital expenses and DSHS took the child support in exchange for the money they paid out in welfare.
Since he is already on the birth certificate as the father, I think the child support division in CA will administratively set and collect the child support for you. He has the right to object to the amount and file a case in superior court, but if he doesn't DCS just takes care of it. If he wanted to go back and contest that he is the father now, he would have to request the court to allow the review. Then if he turns out to be the father, he will probobly pay all the costs.