OK, so rough numbers large you're going to need 600Wh * 3hrs = 1800Wh. Your bog standard 12v LFP battery is 1280Wh so you'll need 2 batteries a day to feed that. The startup load on a compressor is 3-5x the running load but you can probably get away with a 1500-2000w inverter. Bare minimum you're going to want 500+ watts of panel assuming you get 4 hours of aimed clean sun a day.
You're right on the top edge of a 12v system, it might be worth it to go for a 24v based system. If you did that you could get away with a 30a MPPT controller for that.
Granted, this is all assuming that you have no cloudy days and you'll be depleting and charging full pretty much every day and you have nothing in the tank for longer run times or lousy weather. Personally, given the option I'd double up on the panels, SCC, and battery to give yourself more run time and space for cloudy weather.
In short:
Bare Minimum:
2x 12v 100Ah battery
1500w Pure Sine inverter
40a MPPT controller
550w of solar panels
Recommended:
200Ah 24v battery
2000w Pure Sine Inverter
40a MPPT controller
1000w of solar panel
Breakers, fuses, wires, shunt, etc.