It's an interesting experience for me to read expat bloggers' take on making friends with Germans. I've seen opinions originating ranging from the expat who's gone to one local beer festival so she or he thinks she or he's an expert on German life and culture but has no plans to learn the language or to delve deeper in contrast with the opposite, perhaps a person who's married a German, has joined a German club or association, has learned the language, and/or has plenty of German friends.
The latter usually says that Germans are just like anyone else (duh) and that some are more willing to make new friends and others are a bit more reserved about doing so (just as with anyone else). The other category of people who live in Germany but more what I'd call "on the surface" of it have said some...interesting things. To them, becoming friends with Germans is a source of fascination but seems out of reach.
I've read things from them, as well as click bait articles from The Local, that posit that being invited to a German's home will probably never happen as they are way too private for that to happen. Well, maybe if you barely know the person, but in my circle of friends, we enjoy visiting at one another's homes. The only roadblock to this is that sometimes we're too busy or are traveling to get together as much as we'd like.
Another silly thing I've read is that it's almost impossible to make friends with Germans. They have their own lives and aren't necessarily interested in inviting new people into their circle. Again, I haven't found this to be the case. Will the random person you run into the street want to be your friend? That would be weird so maybe not. Frankly, I would find that a bit unusual in the US, too! However, if you're generally not a butthead of a person and you join a club or a social event and you put yourself out there, you'll get to know people and might even make friends -- which is exactly the same in the US.
So, if you'd like to make friends in Germany, the best advice I can give is to join a club or an association. Be friendly but not too pushy. Ask the person if he or she would like to meet up - and be ready to have a specific date in mind and for the first meeting, a public place is best! If you're American, don't pull our bad habit of being vague and saying "we should meet sometime" because the other person is likely to produce a calendar to immediately set up an appointment for a time convenient to both parties. Mean what you say and say what you mean; that's how things usually work here. If you want to make friends, be a good friend yourself. All of these things can be useful for making friends no matter where you are.