Can a person who has been criminally punished apply for immigration to Germany?

Having a criminal record will definitely be detrimental to the application, but it is not necessarily hopeless.

When applying for immigration, if the certificate obtained is that there is no criminal record, it is generally not necessary to indicate it in the immigration application materials. If there is a record of being sued, whether this situation should be explained to the immigration officer in the application materials requires a case study.