The superior white-skinned Indo-European speakers who migrated down into India left their name on the migration route they took. The Arya Varta, the Aryan way. This is recorded in Vedic texts that are at least 4,000 years old, possibly older. tis would kinda sorta indicate that the word "Aryan" that these people called themselves had to predate the invasion of the Indian subcontinent, which happened at least 4,000 years ago, possibly longer.
The original heartland of of the Indo-European language groups is disputed by many mainstream scholars. Most favor an origin in the Caucasus region, which would make Adam's surprise correct, other scholars make a a case for an Anatolian origin of superior white-skinned Indo-European speakers, which would make Adam's surmise incorrect.
I favor the Anatolian theory myself for a number of arcane reasons.