The correct service for physically transporting large amounts of data is Snowball, which is designed to move data into and out of the cloud using secure appliances, speeding up the migration process for large data sets and circumventing high network costs. DataSync would be less viable for the initial bulk transfer due to networking constraints, Database Migration Service is a continuous replication tool for database workloads, and Direct Connect establishes a dedicated network connection but does not provide a physical data transfer solution.