By default email service syncs emails beginning when the service is turned on.
Cirrus Insight provides historical Email Sync for Inbox and Sent folders as a professional service. Contact sales@cirrusinsight.com for a quote. Information that is needed includes the size and number of email boxes to be synced and the service (Outlook or Gmail) in use. If other folders besides Inbox and Sent emails need to be synced the number of folders to sync may impact the cost.