Thank you for your question and sorry you had to wait so long for an answer!
From what I read here, the Embassy of South Soudan does not issue any passport, to anyone, in Germany. You can try and use this argument with the Ausländerbehörde, maybe after asking the Embassy to issue a letter stating this general information.
I recommend you to contact a local legal aid service. You can get in touch with the AWO in the Harburg region, for example.
I hope this helps - don't hesitate to add a comment if you need additional information.
All the best,