identification request - tiny flies invasion

Since they are tiny, this is the best photo I can do:

We are in Berlin, Germany. It has become very hot outside and the flies have invaded us for the last couple days.

The insect is about 1mm long, 0.2mm wide, they are absolutely tiny. They fly but seems to like camping on the ceiling.

The have come in massive numbers, probably over a thousand, but they’re so small we barely see them. They don’t seem to be interested by our food, nor water, etc but rather just stay in cool and darker areas.

Since we have a newborn, I don’t want to use insecticide to get rid of them, so I’m trying to figure out what they are and then.. what to do next 🙂 Right now I am welcoming spiders!