Let's do the math:
A 2000 watt 12 volt inverter, if drawing that power output is using 2000/12 = 167 amps. Your battery is 12 volts and 230 amp hours (usually a rating like that is the C20 rating, meaning that drawing down the battery over 20 hours will provide 2760 watts of power). Lithium commonly have a C1 or C2 rating which may even be 100% capacity of the battery to charge or discharge in 1 hour for a C1 rating. C1 in this case would be 230 amps for 1 hour. Most batteries do not exceed a C1 of 100 amps. If your battery has a C1 of 100 amps (limited by the BMS of the battery), then 100A x 12V = 1200 watts per hour capacity. If this is the case, then your 2,000 watt inverter cannot receive 2,000 watts of power from your battery because it is limited by the math above, again if the BMS is 100 amps max discharge rate. So to output the full 2,000 watts of the inverter, you would need two 12 volt batteries in parallel, providing 12 volts and 200 amps combined of discharge power. But, again, the math says the inverter cannot draw more than 167 amps. The fine print may show a surge capacity for a very short period of time which is greater, but maybe not enough to trip a breaker or blow a fuse.
So, thinking about it, a wire capacity of 150 to 200 amps should do the trick. Bigger wires will only be of benefit if you enlarge your inverter capacity and add battery output.