For millennia, the Indian subcontinent had been divided between different empires which frequently fought against each other for land, power and influence. Between the 18th and 19th century, the entire subcontinent was subjugated to British colonial rule. But then by the 20th century, there was a movement for India's independence.
For such a movement to succeed, the country needed a national identity with which a majority of the people could associate themselves. So how did hundreds of millions of people who had historically associated themselves largely with their religion, caste and language begin to see themselves as part of something larger?
This question is both simple and complex to answer.
The simple answer is the late 19th century.
The complex answer is that it was a long drawn out process which was uneven and unpredictable.
You are more or less correct in saying that for many centuries Indians mainly associated themselves with their religion, caste, locality etc. Of course these broad categories were far more granular, as each caste had sub castes and occupational groups which would vary radically from place to place, and even religion was a peculiarly heterodox identity. Most "Hindus" followed smaller cults that were subsumed within the broad fabric of Hinduism, while in many areas, the people followed different varieties of folk religion that had fuzzy links to both Hinduism and Islam.
So when did this start to change? In the early 19th century, when the East India Company started establishing its colonial rule in the metropolitan centres of Calcutta, Madras and Bombay, they realized that they needed an entire cadre of native clerks and junior officers to augment the various bureaucratic apparatus of rule. While the Company had been collaborating with legions of Indians since the early 18th century to assist in their trade, act as middlemen and to inform them about the country, now they wanted civil servants who would be fluent in English as well. To make this possible, it was adopted as official government policy that western education in the form of English education be taught in schools and colleges established and maintained with Company money. It soon became evident to educated Indians that if they wanted to survive and maybe thrive in this new regime English education was indispensable. it became a sought after commodity and the English educated, employed, middle class person basically started constituting a new social group in the cities. To clarify, an educated intelligentsia was not entirely unknown, the Mughals, Nawabs and Maharajas engaged and employed large groups of such educated men. But the British rule was different. Sanskrit and Persian the two great languages in vogue in Indian elite circles were out of favour. Venerable old Brahmin families or wealthy aristocratic Muslim families were now ineligible as their traditions of learning could not get them a place at the table anymore.
Of course the government could hardly employ all the educated people. By the 1830s and 1840s, this new educated class were present in private British merchant houses, in schools as teachers, as lawyers and doctors, as well as journalists and writers. Newspapers and magazines both in English and Bengali were now published by this class and acted as the mediums of their social discourse. Within this class, education and reading were the marks of status. Naturally they were curious about the history and philosophy of the West that had colonized and crafted them. From the 1830s we see repeated references to various Western political ideas, including nationalism, rights, and liberty. This was followed up by a new curiousity about the history of India. This was the time when James Princep had translated the script used by the Emperor Ashoka and now the heritage of the ancient Maurya empire were at last being talked about. The history being taught to Indian students at this time was based on James Mill's History of India, a book that was written without the author who was an officer in the Company, ever setting foot in India. It was a history replete with British superiority, that depicted India as a land that was stagnant and in decline. In reaction to this, many educated Indians now began trying to find Indian history that was glorious, so they could refute the British orthodoxy.
It was around this time, in 1857, that the Great Revolt happened when large parts of the Companies army, various Indian rulers and feudal lords revolted against and attacked the British. It is notable that this educated class stayed out of the Revolt totally and even condemned it. After the Revolt, when direct British rule was established, there was a proclaimed policy that Indians would get jobs in the Imperial administration. And they did, though they could never be promoted above Deputy magistrate. So while educated Indians were entering the bureaucracy and being posted all over the country, they were also forming political associations to discuss matters of common interest. While early attempts like the Landholders Association were dominated by landlords, the British Indian Association and the Indian Association, established in the 1860s and 1870s were mainly constituted by English educated Indians and they were increasingly vocal about Indian matters. By the 1870s, there were entire genres of patriotic literature, which talked about the glorious past of India, and a very vocal press, both vernacular and English that talked about contemporary issues. And to the educated class, India was now definitely one country. They campaigned against various oppressive acts of the government such as the Vernacular Press Act and the Arms Act. By the 1880s they had formed Indian National Congress (1885), the party that would play a huge role in the Indian freedom struggle.
So by the 1880s and 1890s, the educated class were firmly nationalistic. But what about the huge majority of the population, the hundreds of millions of Indians who lived in the rural areas, who were mostly uneducated and toiled in poverty? For several decades there were only very tenuous connections between them and the educated elite. This divide would change with the entry of Gandhi into Indian politics in the 1920s. He was able to take the idea of a national movement to the rural masses of India and repeatedly mobilize them in vast movements. Of course there are many questions about how the rural people interpreted nationalism in contrast to the educated elite.
So, in conclusion, nationalism was something that developed gradually among a class of western educated elites, and later nationalism would be dispersed throughout the country.
This is a summary, as this is a very large topic.
For further reading the simplest and yet best book I recommend is From Plassey to Partition by Shekhar Bandopadhyay. Its used as a textbook at the undergraduate level and has a comprehensive discussion about this issue.
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