Bear in mind that the contemporary nation state India did not exist as a unified form during the so-called Age of Discovery. Its borders were created in 1947 with the Partition, an event with far-reaching effects and a profound impact at the time on the lives of tens, if not hundreds, of millions. During the "Age of Discovery" the subcontinent was made up of a number of what could be labelled kingdoms, principalities, and an empire, namely, the Mughal Empire in today's Northern India. The subcontinent was, and is, incredibly diverse, religiously, linguistically, economically, etc, and it would be incorrect to flatten all of that it into a single, monolithic worldview.

European contact goes back to the Romans, as ports in today's Gujarat had regular trade with Rome. But as far as the modern era is concerned, the earliest European contact, that is, Europeans traveling the India, was with Jesuits.

As European powers began colonial expeditions and missions, this contact ramped up significantly. But beware of ascribing contemporary European ideas ("Eurocentric", "Indocentric") on early modern and premodern people in India or anywhere, including Europe. This implies that there were somehow shared worldviews across the globe, which is not the case.

Regarding how Indians "characterized the period," due to the swift Anglicization of intellectual life in India beginning in the 18th century with the East India Company establishing a settlement at Fort William (Kolkata) in Bengal, the worldview of the elite in India became the same worldview of the colonizers. The encroachment of the colonizers was slow at first, and it's easy to read about things that took place over a few decades and see a major change, when people living through it may not have noticed it at all. For the Mughal princes and emperors, the Company was a potential economic ally, and for economic reasons the Company was allowed to claim more and more territory and before the weakening Mughal Empire realized what was happening it was too late.

This is a massive question, which requires a substantial essay to answer, but hopefully that helps.

Go-to academic books on this would be Ronald Inden's "Imagining India" or Dirks' "Castes of Mind".

William Dalrymple is good for the non-specialist. For example, his recent book on The Anarchy.

With one of the preeminent aims of Columbian-era travels being finding a seaward route to the Indies in order to establish trade, De Gama’s discovery of the African route must have been impactful news to European courts and naturally caused increased trade to the region.

Do any sources exist that depict the reaction of natives or merchants to south-western coastal India, around Goa and Kolikut? Do any materials exist that document the effects of this initial burst of European trade in the Indian subcontinent in general?