If you bought your car from a second hand dealer, they must by law provide a statutory 3 month 5,000kms warranty but only if the car you bought is less than 10 years old, has travelled less than 160,000kms and is sold for less then the luxury tax thresholdm.
Being that your new purchase has more 200,000kms, even if you bought it from a used car dealer you’d have no statutory warranty to fall back on. But even so, if you did buy it from a reputable used car dealer, it would still be worth discusing the problem with them as they may choose to help, they don’t have to help but they may help.
If you bought it privately, it all depends on what the seller stated or if he made any guarantees. If he did make guarantees and you had it written into the bill of sale, you would have some comeback on him. If nothing was written down, not much chance of getting him to stand by his statements as it would likely be classified as puffery by the courts. In most cases, even with guarantees written in the bill of sale, many private sellers will simply fob you off and it becomes a small claims case (which you’d win).
So you’re likley on your own warranty wise unless you like to fight such issues
In any case if you want your car fixed, as already said, the cause to your start issues could be a Pandora’s box full of problems. So start by disconnecting the battery and checking it’s condition (hopefully RACQ did this check) then charge the battery so it’s full (can take many hours).
Disconnecting the battery will also reset the vehicle electronics (which is a good thing) and when you reconnect the fully charged battery hopefully it has no issues kicking over. If this works but only for a few days, then it’s likley a dead battery cell (which a better test should have picked up) which means a new battery and problem should be solved.
Failing that, get ready to go down the rabbit hole