Yes you can get time to produce caste validity certificates . Apparently you can get admission on provisional basis for NIT on Caste certificate you will share. Incase you have permanent caste certificate by valid authority and stamp then you wont face any issues whatsoever.

http://www.manit.ac.in/sites/default/files/addmissionsection/new%2520pdf%2520m.tech_.pdf&ved=2ahUKEwjp05bCuPHdAhULTY8KHWiaCLgQFjAAegQIBRAB&usg=AOvVaw2j98pOnE7EB7ABIGfqhFQC&cshid=1538816073443