Welcome back to the Wefugees Community and thank you for reaching out to us again.
Indeed, the Jugendamt will most probably ask for the birth certificates of the parents as well. Please see this thread in which a colleague and me provided more information on this topic. It also includes a link of an official website (authorities in Berlin) with a list on the required documents. However, as my colleague mentioned as well, if you can not provide a document (or the respective translation), it does NOT mean that the recognition of the fatherhood is not possible.
I hope this helps and all the best,