How to have custody without going to court or...

You can submit a request to the Head of the Personal Status Prosecution, concerned with requesting to issue an order to include your young son in your custody, attached to the birth certificate of the infant son, and that after conducting the appropriate investigation, the prosecution will issue a reasoned decision to hand over the young child to you.
According to the Personal Status Law as follows:
Article 70
The Public Prosecution may, when a dispute is presented to it regarding the custody of a young child of the age of custody of women, or it requests temporary custody of whom the judgment is due to, or it issues, after conducting an appropriate investigation, a reasoned decision to hand the child over to a person whose interest is with it.