One alternative to the migration path mentioned in other articles is to start with empty mailboxes and migrate just the last X days of mails (for example, 30 days of mails).
Once the cut-over is complete, you can take your time to migrate the older mails either to online mailboxes or directly to archives.
Cloudiway migration benefits
You can use Cloudiway to migrate the last X days of mails if the scenario above matches your needs.
Once the target system is in production, you can migrate the older mails. Your target connector contains an option to Archive mails older than x months which is explained in more detail in other articles of this knowledge base.