We are migrating an existing domain into Zimbra and realize that if we are to recreate their accounts in Zimbra first before updating their MX record to point into our Zimbra public IP, all emails we send to them will get into their Zimbra accounts instead of their existing email accounts on their existing email providers.

Is there a way to overcome this problem so that we don't have to rush creating all their email accounts after updating their MX record to ensure that their emails will not get lost in hyperspace?