Enable this option in the module settings, then click the + icon on the desired date (the icon appears on hover). The article is created on the selected date, using the default time and category defined in your settings.

The date that is filled in follows the Date Field setting of the module. With Start Publishing the publication date is pre-filled, with a custom date field that field is pre-filled, and with Featured Up the featured date is pre-filled and the article is set to Featured right away, because Joomla ignores a featured date on an article that is not featured.