Just to add to @aunt_bea: being a competitive player is not enough. You have to be good enough that the coach wants you. Typically you have to be at Olympian or professional level.
The only sport that I know where several Indians per year are recruited is girls and boys squash. The level at which the top Indians play is enough to get attention from Ivy league coaches. But you’ll have to rank #1 or #2 in all of India, plus win some big international tournaments (British Open, etc).