Can an Indian operator get approval for ETOPS-120 without first getting approval for a lower ETOPS rating? If an A320 aircraft equipped with CFM 56-5B engines is certified capable of 120 minutes ETOPS by the manufacturer as per its AFM, can an Indian operator directly request operational approval for ETOPS-120 from the DGCA? Is this possible without getting approval for a lower rating first, i.e. ETOPS-75 or ETOPS-90?

Note: the request for approval would be based on (a) AFM certification, (b) ETOPS training  to flt. crew and maintenance, (c) implementation of ETOPS maintenance and operational policies and procedures (d) ETOPS CMP compliance, (e) satisfactory in-service reliabilty and operational experience of approx 10 years with a fleet of 15 aircraft on non ETOPS sectors
The short answer is yes (unless the DGCA has some unusual process with no public documentation). But be careful: the manufacturer does not certify an aircraft for ETOPS; only a regulatory agency can do that. The manufacturer can put in its books what it thinks is possible/acceptable, but without approval from the local regulatory authority, an operator cannot legally use those books for continued airworthiness. Generally, though, the big manufacturers work with the big local authorities worldwide to make sure that the books will pass muster internationally. But that does not mean that individual operators are exempt from needing to obtain local certification for their specific operations and airplanes. Given the basis you've listed, an operator would have a very strong case, in my opinion.