Once the baby is born and registered at the Standesamt, he must report himself at the Ausländerbehörde. With the paternity acknowledgement and the custody right of the child, he can ask to go home willingly, therefore ask for a pre-approval (Vorabzustimmung) and the "Grenzüberttritsbescheinigung".
Take all the documents and apply at the German representation in his home country.
Bear in mind that will require much time (processing time)... Depending on his nationality there might be a document review as to establish his identity ( most of the time till 8 months ) prior processing his visa application and for that he will need to exercise patiente.
Once everything sorted that German representation in his home country ... He will be cleared to come back ( family reunion visa).
It is the the right way, it is the best way.
Talk to a lawyer, he might bring much more light on this.