Far more possible if we reduce it to the Indo-Gangetic Plain, excluding the hilly areas in Himachal, Kashmir, and Uttarakhand.
The biggest difficulty to this is that India has been invaded a lot. Before the Muslims, there were the Hepthalites, the Saka, the Kushan, and the Greco-Bactrians. All of them were absorbed into Indian culture to a far larger degree due to an absence of a discrete religion (the Hepthalites and Saka both became Hindu, the Kushan followed a form of Buddhism overlain on top of an odd pantheon of Indic, Iranic, and Hellenic gods, and the Greco-Bactrians were of course Greek Buddhists), but India has been invaded a lot. I think this is why no eternal empire could exist, because if India ever became too wealthy and stable, invaders would come and destroy that stability. China never had that problem because it was sufficiently far away from the steppes except when it really pushed into its frontiers, and by the time the Mongols had the strength to invade, the eternal empire idea was far too rigid. I don't see any easy fix to this issue. I guess, if an empire fortified the Khyber Pass and other invasion routes sufficiently, by the time they fall the eternal empire idea could stick sufficiently that the invaders instead choose to proclaim that they got the *Mandate of Heaven, thus continuing the "eternal empire".
The last Mouryan Emperor was assassinated in front of the Mouryan Army force by the Commander-in-Chief of that Army, Pushyamitra Sunga, who was a Brahmin. He established the Sunga dynasty and persecuted the Buddhists in many ways.
The Shunga barely ruled Maghada, and even that rule was severely threatened by the Indo-Greeks who nearly conquered land as far east as Pataliputra. And really, most historians agree that the Shunga's intolerance was drastically exaggerated by the Indo-Greeks who wished to cast themselves as saviours. They weren't the reason Buddhism died in India, especially when you consider how much it prospered under later kings, especially the Kushan and the Indo-Greeks.
Buddhism prospered strongly in India until the Gupta Empire, a stable period of Hindu revival. If, instead, a revival of the Buddhist Kushan occurred, suffice to say, Vedanta Hinduism would have lost out and India would be Buddhist for posterity. Of course, unlike the Abrahamic religions, Buddhism isn't an exclusivist religion, and so Indians would likely continue to worship gods.