Vistara has other flights and opens a few counters at 2am that will accept your baggage, after which you can get past security and to the airside lounge.

Note that you will be there in the peak wave of travel, usually thousands are either at checkin for the international flights between 11pm and 2am and thousands arrive and want to get out on the morning domestic wave. So things become a cluster around that time.

Arriving at 9.30pm you will get a spot in the landside arrival lounge easily. They have about 8 recliners with a small bench to put your feet on and the area is kept dark. You normally sit there and wait for time to pass. You aim should be to kill time and wait for the mayhem at checkin to subside a bit till about 3.30-4am.