Force Outlook for Mac to sync
Every sync is a full one, so there’s no “force” option. Two things I might try are resetting the local cache (which will purge all the downloads that happened so far) and verifying you don’t have download headers checked.



Your main mailboxes sync by default and your shared mailboxes do not sync, so opt in to sync those if you have any and need them local as well.

The built in help and support would be my next suggestion if clearing the cache and toggling the Download / Sync and then saving prefs and then toggling again with a sync / check.

If you don’t have sync errors and see sync progress (Command 7 and Command 8 menu items), then the issue isn’t on your end, it’s on the server end and you’ll need your exchange admin / help system to engage there.