In contrast to 2015, when the Data Science hype was rolling across Germany, we now do have more and more universities offering specializations or whole degrees in Data Science and tightly related disciplines. Yet, still many aspiring Data Scientists have completed different studies, e.g., computer science, physics, mathematics or economics. To be honest - I highly appreciate the diverse backgrounds of Data Scientists I have been collaborating with.
Coming from a non-DS field, you'll need to do some additional homework in order to keep up with ML natives. But in the age of MOOCs (massive open online courses), there are enough offerings. I'll try to provide an overview and give some guidance.