Can an Indian operator get approval for ETOPS-120 without first getting approval for a lower ETOPS rating?
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.