My first move was from Gmail without a domain so I had to manually move everything, personally I skipped the forwarding step and just spent a while moving everything. Currently I'm using my own domain so moving is just a matter of following the provider-given steps and switching out my email related DNS records which takes a few minutes at most.

Btw mailbox has a guide page for using your own domain: https://kb.mailbox.org/en/private/custom-domains/using-emails-with-a-custom-domain/