No. You're thinking of 2 gauge, not 2/0 gauge. 2/0 is actually 00 gauge, not 2 gauge. Very big difference. 2/0 is 'two ought' meaning 'two zeros'.
4/0 is really fucking huge, almost twice the size of 2/0 and 4 times larger than 2 gauge. Remember, wire sizes get bigger as they go toward zero and then get larger after zero as you get into 0 (1/0), 00 (2/0), 000 (3/0), etc.

2 gauge is more than adequate for most battery relocation, and I wouldn't even bother going larger than 2 gauge because you're not gaining anything. "Bigger is better" isn't always valid. If 2 gauge does the job well, going larger is completely useless and doesn't gain anything except weight, cost, and difficulty routing. You'd have to have a hell of a starter on a hell of an engine and a hell of a long length to need anything bigger than that. This is short duration current remember, so you don't have to worry about constant amperage capacity and current heating and all that stuff.

Basically if the resistance of the wire is low enough to not matter, going to larger wire with lower resistance isn't going to matter any more/less than that. This is like trying to figure out (for example a 250HP turbo setup) whether a 3 inch exhaust is better than a 4 inch (or bigger) exhaust when the 3 inch exhaust has more than enough flow and low enough pressure drop for what you need. You could go 4 inch or larger, but you don't need the flow, it would be more expensive, it's heavier, and good luck trying to fit that under your car.

You're not going to have a wire "burn up on you", don't worry about that. It will get hot for a few seconds during starting, but that's about most current it will ever have going through it and it will cool down after that. Don't use car audio cable for starting systems, use something with a decent insulation quality. Car audio cable may be supple and easy to run, but the insulation isn't very durable or high temp. It's also stupidly expensive because people think they have to pay that price for pretty cable. If you can't find a local place that sells battery cable, try to find welding cable,which works very well also although you might not be able to find it in anything other than black.