Yeah, you could cut tiny pads out of some copper or aluminum sheet and glue them down to the pcb.
You could very carefully scrape the insulation off the vias and tiny traces that went to the old pads and use very thin litz wire (hook wire) to create connections between the new glued pads and the vias/traces (or components on those traces, for example see last two pads on top right where J2 is written, those go to that ceramic capacitor, so you could solder the wires directly to the capacitor terminals).
Looks like there's no traces in the center of the chip so if there aren't traces on the back side of the circuit board you could also use a dremel to make very tiny holes in that area through which you could route very thin wires which would connect the pads to traces or directly to other component terminals instead of using the small vias.
The big trick is LOTS of liquid flux and proper iron tip, you'll want a very narrow one, and a good soldering station. Or a hot air gun.