Hi @Blessingcool
It depends what type of Ausbildung it is. There are two types, one where you just learn at a school (schulische Ausbildung) and one where you learn at a school and also work at a company (duale Ausbildung). The first type is not considered work so you not need permission to do this. The second type is considered work and so you cannot begin this without the permission of the Ausländerbehörde.
It is not clear from your question what exactly you have applied for from the Ausländerbehörde. If you have the status ‘Ausreisepflichtig’, then you cannot receive a work permission to do an Ausbildung. You first need to have the temporary status of Duldung. If you have not done so, I recommend you apply for a Duldung together with permission to work and provide information and proof about the Ausbuildung. Under certain circumstances, you may at a later point be able to change to the more secure status of ‘Ausbildungsduldung’ or residence permit 16g.
Best,
Éanna