Is it possible to solder wires small 0.5mm to 1mm diameter vias?
These are pretty big vias. But every via has a pad around it, 0.1-0.2mm around. Use x-acto knife and carefully scratch out the solder mask around it. Then use a lot of rosin-based flux and regular lead-based solder to make the vias solderable. Glue up a 2x5 0.1" header to the edge or your board for easy and robust access by your test leads. Then solder thin magnet wires ( AWG34-36) from your selected vias to the header pins.  Use low-quality magnet wire, so you don't need to scratch ends - the lacquer will come off naturally under hot soldering iron. That's it.