How can I avoid getting HubSpot email notifications during the migration process?

If you would like to disable email notifications for all CRM users to make sure that no one gets notifications, you can create a preset in HubSpot and assign to all users according to this article.

Alternatively, if you are just looking to avoid getting  email notifications about new records being assigned to you during the migration process,  you can change your personal settings this way: 

To turn off email notifications, go to Settings > Notifications.

On the notification tab, find the Assign section, and make sure that “Email” is unchecked: 

Warning: Don’t forget to switch your email notifications back to ON  or delete the preset after the migration progress is completed.