If you set a date field to be read-only and default it to current date, we have to show the message because we don't know the date the form is submitted until the form is actually submitted.

To get the date to actually appear on the form, you could make the date field editable which would show today's date when the form is opened, but allow the form filler to change it. 

You could also use a date field with current date as the default, then use Javascript to make it read only. The JS read only fields don't allow the user to change the date, and the date would show up on the form. The only catch is, we cannot validate on form submission that the date the form loaded with is still today's date. If the form was loaded on the 10th, but submitted on the 11th, read only JS fields would still show the 10th whereas the read only check box would submit with the 11th.