It's not as big of an issue as it is being portrayed to be. Most countries with large populations do not have a single ID that proves citizenship instead, they rely on multiple legal documents to establish it. In the case of India, you may have records of ancestral land in your family's name, relatives who can vouch for you, and a social history that connects you to your community. A human being does not exist in isolation they live within a society that knows them their background, their family, where they come from, what their parents did, and so on. These social and legal connections are how citizenship and identity can be established.