For a staged migration the MX record should only be changed to point to Office 365 after all mailboxes have been moved.  If you change it prior to moving all mailboxes those that have not been migrated will not receive any mail.

For a staged migration batch to run the mailbox cannot already exist on Office 365.  You could migrate a subset of mailboxes and provision new mailboxes for others and change the MX record.  You don’t have to migrate anything either.  If you set all on-prem users to mail-enabled users you could simply enable all users for Exchange Online and have brand new mailboxes created for everyone.  However, the only migration option to get the remaining users data to their Office 365 exchange mailbox is to use an IMAP migration which only migrates data from a users’ inbox, no calendar or contacts.

Lastly you will always have the option to configuring outlook with the on-prem mailbox and office 365 mailbox and having users manually move what they want to the Office 365 account.

The following video shows details of the migration process: