Possibly a couple of millennia old. And on a much stronger ground compared to most other countries as it is strongly tied to the religion.
Recently I was teaching my 5 year old daughter the basic geography of India. I began with the rivers of the land — Ganga, Yamuna, Kaveri etc. Before I could finish, she immediately caught on as she was taught an ancient mantra from age 1:
गङ्गे च यमुने चैव गोदावरि सरस्वति ।
नर्मदे सिन्धु कावेरि जलेऽस्मिन् संनिधिं कुरु ॥
O Holy Rivers Ganga and Yamuna, and also Godavari and Saraswati,
O Holy Rivers Narmada, Sindhu and Kaveri; Please be Present in this Water (and make it Holy).
The geography lesson of what are the largest rivers and biggest mountains became easy as it was ingrained as part of our daily religious worship. Unlike in other major religions and major countries, in India the religion, culture and our identity as a country are deeply intertwined.
Countries can be defined in terms of politics or through religion/culture and it is latter that last much longer. The Jews could get back to their land after 2000 years as their concept of country transcended politics and etched in religion.
While India is an exonym and doesn’t appear prominently in our local texts, the alternate term “Bharat” appears very prominently in ancient texts. This is an official name of the country used in the Constitution. In our local languages such as Hindi, “Bharat” is the predominant term used for the country.
And the boundaries of Bharat are quite well defined over the millennia that is consistent to this day. Here are the key sites of the country as defined in the ancient epic of Mahabharata.
Every morning across the country the temples begin their prayers worshipping the waters with 7 rivers that defined the land of India to the present day [with just one replacement of Saraswati with Brahmaputra for modern day border adjustment]. Dharmic people in the south include Ganga and Kashi in their prayers while Dharmic people in the north pray to rivers such as Narmada, Kaveri and temples such as Rameswaram.
The largest epic of the country [possibly the longest epic in the world] is the Mahabharata — the story of Bharat. The epic battle in that epic involves kings across the present borders of India.
1400 years ago the great Hindu saint Shankara deeply strengthened the religion and for this he established the key borders. Look at the present borders of India [in Saffron] and how the ancient saint setup his key monasteries.
It is these cultural boundaries and religion that was more relevant for an ordinary person’s life as opposed to what king or landlord to whom you paid taxes to. These were mere administrative entities and not defining your identity. Thus, Dharmic people paid taxes to local kings, Turkic origin Mughals, English company etc at various points of time, but none of those entities really impacted their identity.
While Shankara scaled the Himalayan peaks, he never even attempted to cross the river Sindhu [Indus] or take the boat to nearby Sri Lanka. These were geographically more accessible than the Himalayan peaks, but not culturally relevant for him.
When Shiva worshippers pray to the holiest forms of Shiva, they refer to the 12 key sites that once again define the cultural boundaries of India.
Some zealous Hindus to to the extent of claiming every land near as part of our political geography and this is misguided. The lands to the west or north of present India had very little religious significance for the religion in a long time.