The suggested correct answer is "Use some block-level SAN replication tool to gradually migrate the on-prem historic files to AWS." and explanation says "SAN replication sounds a lot like Storage Gateway which is a reasonable way to migrate historic files to AWS."
That might not work: Say the files are on a 40TB volume on-premises. That volume cannot be replicated to Storage Gateway Volume Gateway because the volume gateway has size limit of 32TB per volume. Also EBS volumes have size limit of 16TB.