Hopefully it should have started by now (this question is a few hours old). Keep in mind that Data Warehouse exports need to wait until all the data is processed.
When pulling a full month of data like this, this can really depend on the timezone that the suite is set to... the export can only start when all the data up to midnight of May 31 for the timezone on your suite has both been collected and processed. Also, it can be delayed by other scheduled reports in your system with higher importance.
At this point, your data should be collected and processed no matter what time zone you are set to... but your queue could still be running through a lot of monthly reports that I can't see based on your screenshot....
