Genetic analysis of mitochondrial DNA in dingoes, and dogs from other regions suggests that the currently extant dingoes in Australia arrived in a single event which was likely around 5,000 years ago (based on the mathematics of the amount of genetic variation present within the dingo samples collected across Australia and fairly solid assumptions about rates of genetic change). The first archaeological evidence of dingoes has been dated to about 3,500 years old, but of course older archaeological evidence of dingoes may yet be uncovered.

Given this timeline - at least 3,500 years ago, likely 5,000 years ago - it appears to be the case that the dingo must have been brought to Australia by sailors (there had been a land bridge between Australia and Papua New Guinea during the last ice age but by 5000 years ago the sea had covered that). My understanding is that the genetic relationships between wild dogs, wolves, and domestic dogs are still somewhat unclear, and in need of further unpacking. So perhaps the links between dingoes and various feral dogs from across Asia can be elucidated further. However, the mitochrondrial DNA subtype most commonly found in dingoes is also found in dogs from, broadly speaking, South East Asia, with a similar subtype found in dogs from a variety of places from Arctic America, to Indonesia and Papua New Guinea, to Japan (but specifically not in the Indian dogs in the sample compared by the researchers).

The dingo having come from Indonesia or Papua New Guinea is...well, probably the most common-sense answer, given the distances involved. It’s simply more likely that a prehistoric sailor might have found their way from Indonesia to Australia than from India to Australia. There is also evidence that dingoes which came to Australia in this era must then have returned to Asia, as a species of lice that originally evolved as a parasite on marsupials is now found in dogs worldwide - so whoever sailed to Australia with dingoes 5,000 years was likely also capable of sailing back to wherever they came from.

Essentially, the dingo, the pariah dogs of India, the Highland Wild Dogs and Singing Dogs of Papua New Guinea and the ancestors of the Japanese dog breed (and internet meme favourite) the shiba inu, are all basically examples of wolves that chose to abandon the hunting lifestyle in order to, basically, scavenge around human settlements/camps/etc. This was fairly common across Asia, and wasn't restricted to India. It has been suggested that the distinctive 'dog' stuff in a dog compared to a wolf is genetically related to behavioural traits in the dog that are advantageous in dealing with humans, and that the dingo has had some doggification compared to wolves, but that further doggification occurred in other animals after the point at which the lineages of Australian dingoes and other dogs diverged.

A recent paper by Bradley Smith and Carla Litchfield which looked at oral traditions and knowledge of dingoes in Aboriginal Australians doesn't really mention any oral traditions about the origins of dingoes, unfortunately, but it does discuss the way that the first peoples of Australia generally did not domesticate the dingo to the extent we would understand today.

The term 'dingo' likely comes from a word spoken by the Eora people of what is now modern-day Sydney, tingo, meaning 'tame'. However, while Aboriginal peoples practiced some selection, in terms of selecting puppies from dingo litters to be hand-reared, and killing off dingoes who were too aggressive to be allowed around campsites, they generally did not selectively breed dingoes, meaning they did not develop all of the further 'domestic' habits of domesticated dogs that their compatriots might have done in Eurasia.

In many Aboriginal societies, the self-reliance of the dingo was seen as important spiritually: "The dingo hunts its own food, makes his own camp, finds his own shelter, and follows his own law". As a result, the hand-reared dingoes reaching maturity were sent away from the camp, rather than trained in a particular activity as they might have been in other societies (e.g., hunting) - though some dogs may have been kept around for their ability to help keep (especially elderly) people warm at night in a 'three dog night' kind of way. Additionally, the dingoes that chose to hang around the human campsites rather than hunt for their own food were seen as a sort of guardian against evil forces.