Leave the current DataMart online while you prepare the new one:
- Create a new database on the DataMart
- ETL-load that database from your DWH while the current database is still online
- Drop the previous database and rename your new one to the old name.
There's still downtime, but you could shrink it to a few seconds this way.
This will require more storage for the extra database, but shrinking outage windows is rarely free.