Dear @Pan 123,
Thank you for sharing your questions with the Wefugee Community!
In Germany, you are entitled to receive Kindergeld (child benefit), in general, if you have a residence permit. If your asylum case is still pending, you are unfortunately not able to get. Also, if you are holding, for example, a residence permit according to §25 Abs. 3 there are additional requirements for receiving it.
The authorities (Familienkasse) will probably also accept a "Auszug aus dem Geburtenregister" from the Standesamt (registry office), which every child normally will receive if they can not issue a birth certificate.
Just another comment from my side: If you are receiving social money from the Jobcenter (ALG II) and you are receiving Kindergeld, the Jobcenter will recalculate and paying less accordingly. I do not know about your personal situation but it might be the case that receiving Kindergeld would not necessarily be an (financial) advantage for you and the child. However, if the Jobcenter is asking you to apply for it, you always have to prove that you did.
I hope this helps and please get back to us with any further questions.
All the best,