Yes, if you have a residence permit under Section 24 (1) of the Residence Act (Aufenthaltsgesetz). As soon as a provisional residence document is issued in accordance with Section 24 (1) of the Residence Act, you are entitled to work. You can then undertake, in principle, any kind of employment in Germany or begin vocational training. Please note that there are certain labor market access restrictions for some professions under German law (e.g. doctors, teachers, educators) in terms of language proficiency, recognition of foreign higher education qualifications and such.
You are also able to start your own business or work as a freelancer. Every industry has specific requirements that need to be taken into account when starting a business. These may include professional law regulations, special licenses and insurance law issues.
If you meet the requirements, you can also directly apply for a residence permit for the purpose of employment or training at the local foreigners authority.
Upon arrival in the matched city, local authorities will advise you on how to arrange for work permit and if needed recognition of documents such as diploma, certificates, references.