A person with subsidiary protection can start a business. Assuming you are registered and receiving financial support from the Agentur für Arbeit or Jobcenter currently, you can receive extra funding from them if setting up your own business. Here is more about it:
There are also various other programmes run to encourage people to set up a business. This can involve a mix of advice, coaching and money (either as a sponsorship or as a loan). Here is an example of the types of supports that are on offer in Berlin:
Here is a good general information portal in English from the German government:
To my knowledge, there isn’t as such a mechanism for converting a university degree into an Ausbildung. An Ausbildung is usually a specific profession (e.g. baker, car mechanic) rather than a general subject area such as economics. Is there a specific Ausbildung you wish to do? As you have a university degree, it may be possible to do a shorter form of training than the full 2-3 years of an Ausbildung. These are called Fortbildungen and Weiterbildungen and can be funded by the Agentur für Arbeit or Jobcenter. They can also supply funding to have your degree translated and recognised as comparable wiih a German one. Here’s more information about that:
You can also apply directly for jobs or internships that require a background in economics. It is ultimately at the discretion of a particular company whether they wish to employ you.