Installing a Nest thermostat without a C wire?
Try the terminal between G and Y on your control board

It looks like the C terminal on your control board is between the G and Y terminals, so I would try there as your first port of call, provided your thermostat cable has spare wires in it.  (It's labeled /C in the bottom row of labels, and has a wire from what likely is your air conditioner compressor running to it already.)