To update the trip's start date, click in the Trip Details (pencil icon next to the itinerary name at the top-left). Next, press into the date and update to the new trip start date and press "Save Changes".
If you would like to add a day to the itinerary, you can do so by clicking "+New Day" at the bottom of the day list.
If you need to add multiple days to the beginning of an itinerary. First, click on +New Day, then press the day details and change the date to the true itinerary start date. This will then add the new days and days in between to the top.
In the example below, the first event is on March 8th but the trip really begins on March 4th, so I need to add days at the beginning like this: