What should a solutions architect do to meet these requirements with the LEAST operational overhead?

Explanations:

AWS Direct Connect provides dedicated network connections, but it is not designed for migrating large volumes of file data. While Direct Connect can facilitate data transfer, it does not provide the specialized tools for moving SMB-based file storage with intricate directory structures, making it unsuitable for this migration.

AWS DataSync is a data transfer service that helps move large amounts of data, but Amazon FSx for Lustre is optimized for high-performance computing workloads and not for SMB-based file storage. Lustre is not ideal for unstructured data with complex file hierarchies, and it may require application changes.

AWS DataSync is an ideal service for migrating large volumes of data, and Amazon FSx for Windows File Server supports the SMB protocol. This solution allows the company to retain its existing file system structure and access methods while migrating data with minimal operational overhead.

While AWS Storage Gateway can help integrate on-premises environments with AWS, the volume gateway is not designed for large-scale file migrations. It is better suited for backup and disaster recovery scenarios. In this case, DataSync is a better choice to handle large-scale data migration without the need for application changes.