Hi @Sachin__Rawat
Yes, it is possible to change from an Ausbildung visa to a work visa. The work visa has to be for qualified work, i.e. a job where an Ausbildung or university degree is required. There are exceptions for citizens of the following countries, who are allowed a work visa for any kind of jobs: Andorra, Austrailia, Israel, Japan, Canada, South Korea, Monaco, New Zealand, San Marino, UK, USA.
Different Ausländerbehörde will have different processing times but 4-5 months for a work visa seems quite long for me. If you find a job, try to make the application for a work permit with all the required documents. The Ausländerbehörde ask the Bundesagentur für Arbeit to check the job conditions but this has to be done within two weeks. After that, you and/or your employer should contact the Ausländerbehörde for updates on the application.
Another option, although quite complicated, is to begin working with your current permit. It allows you to work ten hours a week in a job unrelated to the Ausbildung. You can also work more hours than that if permitted to do so by the Ausländerbehörde. You could then apply for the work permit, which means your Ausbildung permit continues to be valid until they make a decision on your application and you can work in this period.
Best,
Éanna