Most providers have a way of performing a staged onboarding. So Proton, for example, lets you:

1. Add a custom domain name
2. Add mailboxes with the custom domain
3. Periodically gather emails from GMail, etc, to your new mailboxes
4. Create DNS records to allow email to be sent from your custom domain.

...and you can do those in any order at any time without changing the MX records, so your users can switch across to Proton when it suits them. Once everyone is over you can throw the switch on the MX records and kill the GMail service with essentially zero downtime.

I've got a bit of experience with migrating to Proton and Microsoft Exchange but I imagine the vast majority of providers - and certainly those that target enterprise - will support similar workflows.