Thank you for posting.
FileMaker Go will not place any data into the field until you some interact with the date picker. FileMaker Pro behaves the same way.
If you are consistently inputting the current date into these fields you could design your database to auto input the current date when a new record is created. You would still have the ability to change the date with the date picker if you wanted.
In FileMaker Pro, you do not jiggle the date, you click it and it appears in the field. In Go you have to jiggle the date slightly for it to appear. You should be able to click the date in the wheel and it appears in the field