Seems OK. Leaving files on the server implies that they are downloaded in a new Outlook instance. That keeps track of the last time it did it (never) and downloads every after that (all).

The easiest way: just let it do what it wants to do. It's one time only. If it's more than 2 GB, delete enough files from the server to keep it manageable.
Or find out where that timestamp is being stored (I suppose somewhere in the account properties in the registry) and use regedit to change it. I don't know where it is, but I'm sure Microsoft support can tell you if you make the call and pay for it.