Click the pencil next to the field name to open the webform field editor panel on the left.
From the right side field editor panel, choose
Date calendar picker from the
field type dropdown.
In the left side field editor panel, check the check box at the bottom for
Default date to today in order to prefill the webform field with the current date when the submission is accessed.
This option is only available for a
Date calendar picker field type, not a
Date dropdowns type field. Learn more about changing the format of a date field on a webform here.