Indian civilization, just like modern Indian genetics is a mix of all these groups, without one group Indians as a people, or it's civilization doesnt exist. No different to Greece, Persia, Rome.
Invasion, migration this doesnt matter. But a movement of people from the steppes happened and it's linked with both genetics and linguistics.
The fact Latin, Greek, Persian, and Sanskrit have common ancestry isnt coincidence. And recent genetic markers linking North India, Pakistan to Europe and to ancient steppe people's the yamnayas just adds on to it.