I doubt a 600w inverter would reliably handle the startup current for your fridge, and even then, the max run for 8AWG @ ~60A would be ~3.5 ft., (maybe ~6 ft. if frame was used for negative) so not even close with your current wiring.
My batteries were about 15ft. from my transfer switch and breaker panel. I mounted my inverter as close to the battery as possible, (Ended up being under the dash.) and used 2/0 wire to the battery, then ran 12/2 NM from the inverter to my custom transfer switch that only enables the air conditioner when on shore/generator power. (Out of habit, I don't use 14/2 for anything any longer. In this case, I wish I ran 10/2 in case I ever up size my inverter.)
Also, double check the continuous and peek output of your inverter. Some cheap inverters advertise the peek wattage as the inverter's wattage. If it's a high frequency inverter (most are), surge/peek/whatever-they-want-to-call-it numbers should be ignored. Continuous is all that matters in high frequency inverters, and even those, depending on how reputable the manufacturer, should be taken with an appropriately sized block of salt. For motors, like on fridges, you'll want to aggressively oversize your inverter (at least x4 your expected continuous load) if it's a high frequency one -- and make sure the runs to the battery bank, including things like battery disconnect relays, are up to the task. (Low frequency inverters can usually be identified by their size, price and relatively large peek ratings, like over twice the wattage for 20 seconds or so, instead of the milliseconds high frequency inverters can provide.)
Assuming ~170 amp DC peek, and you're running both a new positive (+) and negative (-) wire from inverter to the battery (not using a short negative jumper to frame), you can run (per run):
~5 ft. of 2 AWG Copper Welding Cable (~10 ft. total for both + and -)
~6.5 ft. of 1 AWG Copper Welding Cable (~13 ft. total for both + and -)
~8 ft. of 1/0 AWG Copper Welding Cable (~16 ft. total for both + and -)
~10 ft. of 2/0 AWG Copper Welding Cable (~20 ft. total for both + and -)
You can stretch those a bit, (and even a bit more if the RV frame is used for negative path) but I wouldn't push it too far. It's always better to oversize the cable. And make sure it's copper cable -- not aluminum or copper clad.
If you can get the inverter close enough to the battery, these are a relatively cheap and available option:
https://www.harborfreight.com/3-ft-i...awg-63748.html