The answer to this question depends on what you mean by India. Geologically speaking, the Indian Craton formed when it broke away from Pangea during the Jurassic Period about 160 million years ago and then separated from Gondwana 125 million years ago.
The first human inhabitants of what is now India arrived around about 75,000 years ago, although this claim has been disputed. Concrete archaeological evidence suggests that humans certainly were in the region as early as 30,000 years ago. These were likely migratory stone age hunter-gatherers. The earliest known permanent settlements date to about 9,000 years ago at the Bhimbetka rock shelters, which feature some of the best preserved cave paintings of the period.
Around 2500 BCE, the first civilizations were founded there with the establishment of the Indus River Civilization. This civilization built some of the earliest known cities in the world. It thrived until around the end of the Bronze Age around 1500 BCE.
The modern state of India dates to 1947 when India won its independence from Great Britain. It was partitioned that year into the two independent states of India and Pakistan (Pakistan was later partitioned into the two nations of Bangladesh and Pakistan).