What it costs
Dual running and non-production are the two costs that consistently surprise people.
Estimate the target service, data transfer, storage and retrieval, synchronisation and replication licensing, non-production environments, and delivery operations. Give each estimate an owner, a date and its assumptions.
The two costs that consistently surprise people:
Dual running. Any period of coexistence means paying for both platforms plus the machinery that keeps them consistent. If waves or a long stabilisation period stretch, this is where the budget goes. Cost the coexistence period explicitly, and cost the scenario where it runs 50% longer than planned.
Non-production. Rehearsal at representative scale means an environment at something like representative scale. Teams budget the production target carefully and then discover the test environment was not free.