Using the New Outlook for Mac for personal email and calendar
I would first try creating a fresh Outlook profile without opening Outlook: open Finder > Applications, right-click Microsoft Outlook > Show Package Contents, then open Contents > SharedSupport > Outlook Profile Manager. Create a new profile, set it as the default, and try Outlook again.
If it doesn't work, please post a screenshot of the exact Repair dialog, because the wording may identify whether this is an Outlook profile/database repair prompt or an application/installation problem.