Many German employers prefer hiring people they have already seen at work. If you hold a Praktikum or Werkstudent position, treat the last third of the placement as a quiet campaign: ask for a mid-point feedback talk, volunteer for one visible deliverable, and learn how headcount decisions are timed in that team.
Do not wait until your last day to ask about openings. A calm conversation with your supervisor two to four weeks before the end is usually enough to learn whether a full-time path exists—or which sister teams are hiring.
Keep a short record of tasks and outcomes. When the conversation happens, you can point to concrete work rather than enthusiasm alone.