Child advocates would remove the child from the custody of his mother when they discovered she was shacking with a guy (not the childs father) in a barn. In most jurisdictions that would constitute child neglect.
Of course, Mary would have an underpaid court appointed attorney to represent her in the dependent-neglect proceeding, and Joseph would be out of luck once it was determined that paternity could not be established within a reasonable degree of medical certainty through blood or DNA testing (97% probability that Joe was the dad is sufficient, but absent divine intervention, that couldnt happen, hmmm?).
He would be excluded from juvenile court as a stranger to the proceeding and investigated for possible sexual deviance (all those oxen and asses around), and he would be told that he had no standing to object since he was not the natural father of the child and was not yet married to Mary (by their own admissions they had not yet consummated their union).
The Division of Children and Family Services would ask the court to order Mary to take parenting classes, and the Court would order that homemaker services be provided as well, since obviously Mary cant keep house properly (the place where the DHS workers found the child was kept remarkably like a barn).
Mary would be allowed to have one visit with Jesus per week at the Centers for Youth and Families. The visit would be one hour long, and supervised by a therapist since Jesus would no doubt be put in therapeutic foster care to prevent psychological damage resulting from the horrible lack of civilization to which he had been exposed at such a tender age.
At the eighteen month dispositional hearing, the court would consider terminating parental rights because of Marys refusal to bring a paternity suit against Jesus true biological father (or even to identify him to the satisfaction of the Court).
The Court would be appalled at the life choices Mary would have made: she would have completed her marriage to Joseph (that suspected sexual deviant) and had more children by him, which was obviously contrary to Jesus best interest.
Since Mary and Joseph had fled the jurisdiction with Jesus once to escape encounters with the authorities, they would determine that Mary and Joe had nefarious plans to abscond with the Ward of the State to Egypt again, where they would possibly engage in dangerous and illegal activities with him. Parental rights would be terminated, and Jesus would be put up for adoption.
He would be adopted by the Herods, a well-connected and politically powerful family, who have been searching for just such a child as Jesus.
Of course, Jesus will die in the custody of his adoptive family, because thats all they wanted him for in the first place. Social services will NOT have intervened prior to his death because the state social workers could never imagine someone as highly placed as the Herods exploiting children or torturing them to death.
The political ramifications for the Herods would have been too severe. In all likelihood, the social service agencies would cover up the death as one occurring from accident, and Herods good name will be preserved.