Initialization failed with exception: Microsoft.Exchange.EdgeSync.Common.EdgeSyncServiceConfigNotFoundException: Couldn't find EdgeSync service configuration object for the site SiteName. If the configuration object doesn't exist in the Active Directory location CN=EdgeSyncService,CN=SiteName,CN=Sites,CN=Configuration,DC=domain,DC=local, create it using the New-EdgeSyncServiceConfig cmdlet. If the object does exist, check its permissions.. If this warning frequently occurs, contact Microsoft Product Support.
The server was moved to a new site. Like the event says, "New-EdgeSyncServiceConfig" needs to be run from the Exchange shell to create a config for the new site.
[PS] C:\>New-EdgeSyncServiceConfig -Site SiteName