I went through the other answers and I agree with most of them.
Yes, you can do a part time job with basic German speaking skills and earn enough to get by. With A1 level of German, I have worked as a street cleaner to clear snow in winter, packed frozen food for 8 hours a day and taken up night shifts at a garment warehouse doing inventory work.
But if you want to have an edge over your competitors and get a part time job of your choice, that might also help further your career in addition to providing you more salary than a basic job that requires no skills, speaking good German is necessary. Once I improved my German (and had some good luck, i.e. an awesome girlfriend) I was able to work in a company close to my vocational field and then based on that job got an internship and that in turn earned me a student job at the university which paid almost double of the basic jobs.
I would also implore master students who have newly moved to Germany, to take a semester or two to settle down, get integrated into their study programs, build a network and learn German before rushing headlong into part time job search and losing sight of why they moved to Germany in the first place. You're here to study and build a career. It is a big step, moving from your home country to Germany. Savour the experience of living and studying in a new country with new culture and learn the local language. Once all that is taken care of, you will definitely find yourself a good part time job to keep yourself financially afloat. Good luck!
