There is a difference between invasion and migration though, AIT has long been debunked, the current consensus is AMT

There are many historical events of Indo-European speakers invading India from the north, like Darius the Great, Alexander the Great, the Mughals. AIT refers to a theory from an earlier time period but rejecting it does not rule out subsequent Indo-European conquests of the region which surely contributed to the spread of Indo-European culture and language southward.