Letter of recommendation from professors without prior contact
Yes, it is silly. Boneheaded, actually. I assume that they don't want many applicants and I wouldn't put a lot of hopes on this position.
But you might ask some of your current colleagues for advice. It might be that your work has been shared with other German scholars who might be able to provide a (mild) recommendation based on your published work.
You could also ask for an exception, explaining your situation. Some other arrangement might be made to happen if you, otherwise, seem like a good candidate.
Good luck and keep looking.