Here is the math -
12.8v battery - you mention 300amp output on the BMS with surge to 500amps.
Ordinarily I suggest fusing against the max current of the BMS - not the surge - the fuse will hold up under a surge if sized right. But at 300amps the other factor is the inverter you are choosing.
300a * 12.8v = 3840W --- is your inverter 3000w? 3500w?
Fuse based on the math is
300a * 1.25 = 375amps
But if your inverter is smaller than that say 2000w
2000w / 12.8v = 156a * 1.25 = 195w - so you fuse at 200amps.
2500w / 12.8a = 195a * 1.25 = 244amps = fuse at 250amps.
Various wire tables here
https://diysolarforum.com/threads/robbob2112-answer-thread.84402/post-1286275
Welding wire for 375amps is 4/0
Welding wire for 250amps is 1/0
Welding wire for 200amps is 2awg
Now the 200amp and 250amp wire sizes are right close to the edge of capacity so you step up one size so they run cool and can respond to surges.
So 2/0 for 250amp and 1/0 for 200amps .
You can't go wrong oversizing the wire and fuse to your needs, it will cost a bit more but will run cooler. Fuses have more resistance as they decrease in amp capacity so the class T for 370amps will run cooler than ther class T for 200amps for the same current pushed through it. But you can't upsize the fuse without also upsizing the wire.
The major drag about larger wires is they are harder to fit and bend in tight places.
For welding wire windy nation is the place to go and for battery wire batterycableusa is a good place. You can get raw cable, or of you know the length you can get them pre-crimped with whatever lugs you want.... this is where the tight spaces can be handled by getting them to crimp lugs that bend at 45 or 90 degrees or a left or right bend to be able to just bolt them down.
If you decide to make your own cables buy a good Temco or other quality hydraulic crimper... don't waste your money on the cheap AMZCNC or other junk on amazon - it will make bad crimps and wings... and the lugs by Ancor, Temco, Selterm, and a few others are fine... if the name of the vendor sounds like a frypan hit the wall and bounced twice it will be undersize, oversized, or thin...
