Welcome to the Wefugees Community and thank you for your very interesting question.
In general, you need to have a temporary residence permit for at least 3 years (for refugees) and 5 for other types of residence permits before you may be granted the permanent residence permit (Niederlassungserlaubnis). But as you can also read here, the period of the asylum process may be counted as well. I am thinking now, if the whole period of the pending court decision could be counted too. But as I really don't know, I will link 2 of our experts here. Dear @alla_fka or @mbeon-Ruth, do you have any answer or advice on this?
However, you will always need to apply for the permanent settlement and also fulfill all the other requirements - which you can also read in many threads on this platform or the link shared above. The authorities will for sure not issue the permanent residence from their initiative.
I hope this helps and I am looking forward also to our experts' reply.
All the best,