Not directly after your studies, but there is a path to get PR in Germany after completing your education. Here’s the breakdown:

• You cannot apply for PR directly upon finishing your studies.
• You will need to find a job in Germany related to your field of study (or not necessarily related for some professions).
• Once you have a job, you can apply for a work residence permit.
• After holding a work residence permit and working in Germany for a specific period, you can then apply for PR.