But you’re right in the broader sense, that Indian people feel that India has been around for longer even if it hasn’t. That is arguably more important to keeping the nation together than anything else.
Now depending how you're counting, and your definition of empire the Roman empire had a continuous history (with radical transformations over time but nevertheless continuous) for 2000 years.
But hey, it all depends on how you define things. Undoubtedly the Indian subcontinent produced an incredibly deep and rich cultural history that spanned thousands of years.
It was just slightly more fractured and dynamic. The Romans objectively held their firm (and often brutal) hold on a lot of land for a lot of time with a continuous identity, in a way that is not just to say that the same common culture continued on across various political arrangements that changed over time. Because I'd that's what we're talking about we could say that the whole of Europe has a kind of cultural union (fostered by the shared religion) that continued on till today.
But the details of how you define things matter of course. Today you wouldn't consider the byzantine empire to be the Roman empire, but ask somebody from the 1300s living somewhere in the aegean see or anatolia and they will tell you they were Romans.
What is the "Indian Empire"? The Mughal Empire? That lasted like 300 years.
Not locations.
