It’s not clear what you mean by “native people”. How far back does one have to go in order to qualify as “native”? Ten generations? Twenty? A hundred?

If you mean “Are Dravidians the original inhabitants of India” in the sense of asking if they were the first humans to enter India, then the answer is emphatically no.

Current understanding is that modern humans spread out from Africa around 65,000 years ago. They followed a southern coastal route eastwards across Asia, including India. So India was part of the ancient migration corridor, and there were modern humans in India at least 50,000 years ago. There are human remains in Sri Lanka dating from the middle Paleolithic; genetics studies show that the Andaman populations have been in place for at least 30,000 years. All of these island populations appeared after the Indian mainland was already populated, meaning that there were humans in India long before these events. In fact, it’s possible there were even earlier waves of migration, since modern human tools dating from 75,000 years have been found in India.

This is long before Dravidians existed, long before any identifiable group of people in the modern world existed.

If you mean which group of modern Indians existing today have the longest ancestry in India, the answer would be the Australasian people, who are represented by certain Indian tribes such as Bhils, Gonds, etc. They are part of the same migration that settled the Andaman and Nicobar Islands, which happened at least 30,000 years ago. Of course, unlike the islanders, mainland Australoasian people have mingled substantially with populations that arrived later, so their ancestry is now also mixed. But they have the highest ratio of the oldest admixture that we can find in Indians today.

In contrast, Dravidians and north Indians are much more recent arrivals in India. The exact origin of Dravidian populations is unknown, but genetically they share certain features with certain populations from the Mediterranean. Ancient demographic models indicate that around 10,000 – 20,000 years ago, there existed a genetically related population in a belt that stretched from the southern Mediterranean to India, and Dravidians may be descendants of this group. Of course, 20,000 years ago none of the modern populations existed, so we are talking about a proto-population that looked nothing like modern Dravidians or modern Mediterraneans, but were ancestral to both. The extent to which populations have diverged today represents thousands of years of adaptation, plus extensive intermixing with geographical neighbors. In India, Dravidians would have mixed with the tribal populations I mentioned earlier, which is also borne out by genetics.

People continued to arrive in India throughout history and prehistory, even after the Dravidians. Most north Indians are relatively more recent arrivals than the Dravidians, from central Asia, Iran, and further west. On an individual level, you could point to specific individuals who have very recent ancestry in India, and are more related to say Iranians. On a population level, it’s all about statistical admixtures, and on average, north Indians have about 10-20% more recent west Asian/European ancestry than south Indians, depending on caste.

So it kind of depends on when you impose your cut-off limit for “native Indians”. Any date is bound to be arbitrary. However, if you modify your question to “what is the oldest currently existing lineage in India today, and who has it”, then the answer would be Australoasian, and the people who have the highest admixture of this lineage are tribal groups like the Bhils and Gonds.