BGA prototyping practices
0.5mm BGA gets expensive: look here page 11.

If you do it properly (as shown in the document) you'll need vias with 0.12mm drill and 0.25mm pad. This is not basic cheap PCB prototyping, it's real high quality manufacturing. You can get 4-layer for $40 these days, but not with these tolerances, this will cost several hundreds.

If you put the solder balls on top of vias the solder will get sucked in, I don't know if it would work.

I'd recommend a BGA prototyping board but couldn't find any in 0.5mm pitch. YMMV. It may very well be cheaper to buy the chip manufacturers' eval board.