Getting a job while learning language for authorisation

Hello, I need other people's view on this
I am a doctor from my home country and presently in Denmark for the authorisation process. Everything seems okay asides the getting a side job part. The rule is that your residence permit doesn't allow you to work, and if you want to work, then you must apply for a work permit. To apply for a work permit, you need get a job contract from an employer and the employer needs to fill a part of the application form ar1 before you can submit your application for work permit to SIRI. This seems to be impossible as most employers are not ready to do that. The ones who were able to give job contracts find it difficult filling the AR1 form from SIRI.
So, please, how has anyone in this category been able to get through this stage? One can't survive in Copenhagen for the duration of language learning without any job atleast.
Hope to read from anyone who has an idea on how to solve this part of the process.