I think it’s important to take things into our own hands to whatever degree we feel able to. I don’t invite my neighbors in my building for tea or knock on their doors but I smile at them or make comments to show that I don’t have anything but good will.
This actually reminded me of something I forgot to mention! When I was living in Georgia, I came to discover a culture so different to anything I had ever known that the people did not smile. They considered it fake. Naturally, close friends or relatives would smile and greet each other, but a stranger smiling to another in the hallway of the building or greeting them would be something they'd instantly reject. They'd ignore you or go as far as not even looking at you back.
I found it so strange, especially when I'd see the same people almost every day in the small apartment building I lived in. And it made those cold hallways feel far more cold. More isolating. And it was often the same way when you went to a cafe. Those were probably the worst neighbours I've had, for sure.