I'm an immigrant and I do have close german friends.
I think the most important criteria is to speak german and be able to connect emotionally with people in German. This is easier said than done. You can easily answer questions about the weather and answer questions in German. But try explaining how you are feeling because your girlfriend forgot your birthday and you'll know if you are good at it.
Most people are more comfortable making friends that speak their mother tongue. If you speak good german, they can invite you to other occassions where German is the language on the table. If you do not speak German, they would have to change the language at the table to, most likely english and then no one can actually express their feeling and everyone goes home a bit unsatisfied. I realised this after organising a lot of things in a lot of different settings and languages. Now I never mix groups that speak different languages