As it is spelled out in the specifications you bring up the backfill in 6" lifts compacting each lift before adding the next lift. The round trenchbox system is raised with every lift.

Resource Link: https://mrmanhole.com/product/cookie-lifter/
Additional Link: https://mrmanhole.com/wp-content/uploads/2021/11/Sample-Specification-Utility-Access-Concrete.pdf