In Outlook 2013, is there a way to run AutoArchive immediately?

Solution 1:

Is the manual archive option what you're looking for? If so, it's available from File / Info / Cleanup Tools / Archive:

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Solution 2:

I'm sure you already found the answer to this.

But for others that may be looking.

FILE -> MAILBOX CLEANUP -> MAILBOX CLEANUP -> AUTO ARCHIVE

This will start the process immediately.