The administration of the institute does not make this decision.
This decision as to when the classes of the first year can commence is taken by the Joint Seat Allocation Authority (JOSAA) which is in charge of the admission process. The institute can make the decision from the second year onwards.
Generally, the classes will start a week after all the counseling rounds have been concluded. They usually begin at the end of July. The classes for the first year in the NITs start together.
It would be preferable if you come one or two days prior to the beginning of the classes to get acquainted. That is if you are planning to live in the hostel.