The correct service is Storage Gateway because it enables integration of on-premises applications with cloud storage by supporting common storage protocols such as NFS, SMB, and iSCSI. This facilitates a smooth extension of on-premises storage to the cloud, which is beneficial for cost-optimized storage strategies. DataSync is mainly focused on the efficient transfer of data between on-premises and the cloud and is not primarily used for real-time access. FSx provides fully managed native third-party file system services, but it doesn't provide a direct hybrid storage solution. EBS is designed for use with EC2 instances for block storage and does not fit the hybrid storage integration scenario described.