There was direct trade between Mesopotamia and India from the 3rd millennium BCE, and indirect trade as far back as the 9th millennium BCE.
I'm wondering what effect the Bronze Age collapse (c. 1200 BCE) had on this trade, and on India in general. The article I linked to says trade with the Indus River valley was disrupted around 1900 BCE, but I find it hard to believe that all ME-Indian trade stopped. Surely, indirect trade routes survived, and maybe direct trade with nearer regions such as Persia continued as well.
I don't know enough about Vedic India to say how much it traded with Mesopotamia, or if it was harmed by the Bronze Age collapse. It seems like this was a time of slow state-building in the north, and continued prehistory in the south.