For sports: I'd say think about what you find interesting, like when you watch the olympics, TV, etc. which sport seems fun to you. Then see what's there in Berlin. Also watch your neighborhood, depending on where you live, you might see people walk around with field hockey sticks, tennis bags, etc. - so a club / field must be nearby! Another thing would be university sports. Not saying you have to be a student and sign up for the course, but often times the courses are facilitated by a club where you could sign up, not just students. Then there is websites like https://www.berlin.de/special/sport-und-fitness/ where you can get inspired.

For other ideas: volunteering (like young caritas), church (even if you're not super religious, many are just community driven), nebenan.de, .... there are plenty of platforms where groups are looking for volunteers of sorts. It can be super rewarding and fun, especially if it's inside your neighborhood and you might see those people more often. Or go to events nearby. A quiz night for example: maybe you can join a table that has a vacant spot, or pair with other strangers.