The cable length and amperage determine the wire size needed. Online calculators are available. Search or voltage drop calculator. If you plug in 3000w, that should be a bit conservative for you 2000w inverter but if not significantly more, look at going on size larger.
At 3000w, you are pretty much up around what the starter on a car will pull, so yes, you need a thick cable.
You might look for a heavy duty set of jumper cables to sacrifice. Much smaller 50amp charger installed recently but the 6ft 4 gauge wire was running $30 per cable (ie: I needed 2). Set of jumper cables was $15. I cut the ends off and used the wire.