Hi @Lily,
Based on my research, you can work as a dental assistant without an Ausbildung. It is not one of the protected professions in Germany (e.g. doctor), where a specific qualification is required. However, it is likely you will not be allowed perform certain tasks such as x-rays. You can also take the final exams to have the ZFA qualification as an external candidate.
If you residency is based on the Ausbildung, then you will only be able to change your permit to a work permit if you have a qualification either from Germany or a recognised one from another country. A job as a ZFA without a qualification will not unfortunately not be enough to obtain a permit.
You mentioned financial difficulty with the Ausbildung. Have you looked into the possibility of getting the BAB support payment for people doing an Ausbildung? However, it is quite restrictive in accessing it for non-Germans.
Best,
Éanna