The fundamental challenge of server migration is singular: servers continue writing while you're copying their disks. If a 50TB disk takes 24 hours to copy, when the copy finishes, the original and copy differ by 24 hours of changes. Catching up on that "final delta" is the technical challenge of Cutover.
AWS Application Migration Service (MGN) solves this with block-level continuous replication. It copies the entire disk initially, then tracks all subsequent changes in real-time and applies them to an AWS Staging Area. At the moment of Cutover, the "final delta" is measured in seconds.