It is not possible to apply for the first semester to be the summer semester. Applications for the first semester can only be submitted for the winter semester.

However, applications for higher semesters in the summer semester are possible. For the requirements, see https://www.stat.de/archives/ufaqs/can-i-apply-for-higher-study-semesters-hohere-fachsemester .

Otherwise, you can register as guest student (“Nebenhörer”) and take some courses in the summer semester and before applying for the winter term. For HU, see the course guidance centre on the HU website.