Most judges are aware that women lie. Hire an investigator. Even half-***#d investigators can find 90% of people in 4-8 hours of searching unless they are persons who live 'off the grid'.
That said, if you can prove abandonment, then I think CA's statute for stripping parental rights based on abandonment is 3 years. You need proof that he knew there was a child and that he knew the child was his. Generally, this involves having filed for child support, but I know of cases where the witness was the paternal grandmother.