Teaching is a special field. There is a program at the university of Potsdam that could help you with that. It enables you to continue your studies and to gather teaching experience. Since a very good level of German is required in order to become a teacher, there is German classes included in this program. As far as I know it does not matter how well your German already is because you can start on various levels.
The problem is that this program was full really quick. So maybe you should ask the university if there are similar programs or cooperations at other universities. You can just send them a mail in english and ask if there are possible ways for you to start studying and if an Aufenthaltstitel is required or not.
Apart from that it is probably possible to join classes as a so called “Gasthörer” (guest listener) to get to know how german universities and their lectures work etc.
Another way would be to try out the Kiron Online University. There you can study by using online/video classes.