Dear @Andrey_Malk,
Welcome to the Wefugees Community and thank you for your question.
In general, you can apply for the "Ausbildungsduldung" up to seven months before the start of the training (Ausbildung) and obtain it up to six months before the start. You are right, people from so-called safe countries of origin (and who applied for asylum) are usually not allowed to work and subsequently don't receive an "Ausbildungsduldung". Handbook Germany is also providing very good information on this topic.
I also read that the German government is planning to declare Georgia and Moldova as safe countries. As far as I know, they didn't finally decide on it yet though (and therefore did't implement it either). But I agree that you should observe the developments carefully in that respect.
Do I understand correctly, however, that you are still in the asylum procedure and you are holding an "Aufenthaltsgestattung"? In that case it may make sense to withdraw your aslyum application. But please discuss this carefully with a lawyer or with experts in a very experienced migration counselling office.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,
Meike