First of all, cooperating with the authorities by clearing your identity and providing a passport is essential not only for getting the Ausbildungsduldung (which is naturally the aim, if you are to start Ausbildung, because it brings safety) but also for getting and keeping a permission for any occupation (work or Ausbildung). The worst thing is to do nothing for documents, you risk not to have a permission for Ausbildung at all and even to get a bad Duldung for people with unclear identity (worst scenario).
If you already have a passport, be careful. If the Ausländerbehörde finds out that you had it and didn’t provided it at once, you will have a big problem, because it is your duty in the German law to give them your passport if you have it. So if you bring your passport to the Ausländerbehörde, they must think, you didn’t have it before (or at least no proof of the opposite).
If you first have to apply for your passport in the embassy, it gives you some time. It is not good, if you didn’t give any documents to the Ausländerbehörde and your identity is absolutely unclear. In this case you must try to get a birth certificate or other good documents as soon as possible. And you must note all the steps you make to get documents and inform the Ausländerbehörde what you do, especially if you have a dead line for that. Don’t miss the deadline without giving them information that you do everything in your power.
If you have an offer for Ausbildung from a building company, give it to Ausländerbehörde and ask for permission 1) to make this Ausbildung 2) to move to another federal country for that. It is difficult to say, how cooperative your Ausländerbehörde is. Anyway, if they have nothing against it, they have to ask the Ausländerbehörde in the place of your Ausbildung to agree to your moving there. But I hope, this last point won’t be a big problem.
They can give you a preliminary permission with the condition to bring documents. After 3 months with a normal Duldung you can apply for Ausbildungsduldung – naturally under the condition that you get a permission for this Ausbildung. In this moment it is mostly essential to give a passport, even if it is a risk.
There is one more point to stress. If you came to Germany after the 31.12.2016, your identity had to be cleared (not necessarily with a passport, but with other essential documents) until the 30.06.2020. So, if you didn’t give any documents at all before this date without a good reason why, it can be a reason to reject Ausbildungsduldung, even if you provide now. On the other hand, it is in discretionary power of Ausländerbehörde to give you Ausbildungsduldung, if you bring documents now, so you anyway must try everything possible.
These laws are really very complicated and, additionally, many things just depend on the position of your Ausländerbehörde. It is impossible to assess in online consulting how much risk you have in this or that case and what moment is better. For that you must look for a good councelling center in your area, who can analyse your whole situation, seeing your documents, letters etc. To take a good lawyer is the best option, but it is certainly not cheap. Perhaps there is a free of charge legal councelling somewhere near you.