Hi, I have migrated more than ten organizations to google apps and have been an email server administrator for more than seven years across various freelance platforms.
I will create your mailboxes in google apps first then change MX records. Then you will have all new emails in google apps and old emails in old hosting. I will next migrate old emails to google apps by imapsync. This ensures you lose no email in old hosting after MX is changed and DNS cache not flushed by sender servers.
Regards,
Tutul Barua