It does not matter in which Adobe tool the form is displayed, auto-generating a date is the same. It's done with a document level script. The trick is to get the script into the PDF.
this.getField("MyDateField").value = util.printd("mm/dd/yyyy",new Date());
If you cannot edit the doc scripts , then open the console window and run this code.
var cJS = 'this.getField("MyDateField").value = util.printd("mm/dd/yyyy",new Date());';
Where "MyDateField" is the name of the field you want to put the date into.
The source for PDF Scripting Info pdfscripting.com
The Console Window (Video tutorial)
The Console Window(article)
Having trouble, Why Doesn't my Script Work