How to set calendar to Today automatically on dropdown

I am using the datetimeditbox and its value is iitialized to Datetime minimum (new DateTime). This means that on the edit box one see  0001-011T0:00:0; (using "s" format). This is exactly what I want. However when I click on the dropdown the selected time is sometime in January 1753. I would like the selected value to be today's value (without changing the value on the edit box of course). In other words I would like to automatically "click" on the CalendarTodayButton when user clicks on the dropdown.

I have not found a way to achieve that. Any code sample?

Thanks.