Mycenaean Greece was a Greek culture, and it was literate at that, though we know none of its literature. The Homeric epics preserve bits and pieces of that culture orally.
But Greek civilisation as we understand it is based on written records, and those written records start with the invention of the alphabet: 8th century BC. Let’s make it 7th century BC for actual literature that wasn’t orally transmitted.
What was India doing in the 7th century BC?
From a cursory glance at Wikipedia, India was moving on from Vedic culture to new religions (Śramaṇa) and new systematisations of the old religion (Upanishads), new political structures (Mahajanapada) and new settlements (Iron-Age: Brief Notes on the Second Urbanization in India). The modern tradition of writing in India seems to date from the 4th century BC, but the oral texts of the Vedas, Upanishads, and Epics seem to have been much more extensive than the Greek Epics.