Almost done with my Ausbildung but I'm switching employers directly after. Need help with bureaucracy.

Hi everyone. I'm currently doing a nursing Ausbildung (vocational training) which I'll be finishing in the end of September. I don't plan on staying with my current Trainer/Ausbilder so I already applied elsewhere. I found an employer and got a contract in a different state from the one I'm in (I'm currently in Niedersachsen and the new employer is in Berlin). My contract is signed and I'm set to start on the 1st of October.

Here's the tricky part: I currently have a residence permit tied to the vocational training which ends on September 30th September). In order to legally work as a nurse at my new place of work I'd require a worker's permit issued from the Foreigner's authority in Berlin. However, since I don't get my Certificate which allows me to work as a nurse till the middle of September (when I hopefully pass my exams) I technically won't be able to get/apply for a residence permit until the middle of September. That means I would have a two week window to have my residence permit changed from Vocational training to a Worker's permit, which I know is unrealistic. Which is why I would like to know if there's a specific way I could go about this that would somehow ensure I get my new residence permit on time?

Would it be possible to apply for a job seeker's residence permit here in Niedersachsen and work as a nurse with that? How do I go about the transition from Vocational training visa to a Worker's visa, since the Foreigner's authority in niedersachsen technically would no longer be responsible for me. Do I need to make all applications in Berlin? Can I somehow apply for the Worker's permit in advance? (to be specific with the expectation of passing my exams and getting my certificate afterwards)