The correct answer is C. Deploying an S3 File Gateway on premises and creating a new NFS file share on the gateway allows seamless migration of data from the existing NFS share to Amazon S3 with minimal bandwidth usage. This solution is efficient for large-scale data migration because it leverages local network transfer initially and then synchronizes with S3. The other options either involve more complex setup (D) or cannot efficiently handle such large volumes of data (A). Option B is also a feasible solution but relies on physical transport, which may not be as immediate as the S3 File Gateway method.