Based on weather forecasts (which, at the time, could not reliably extend past 48 hours), a June 5th departure was impossible. (The link depicts the actual weather map for 5 June 1944.) The worst weather in twenty years had descended on the English Channel.
Then ... almost miraculous news was reported by a Royal Navy ship, stationed due south of Iceland.
Despite the current weather, the ship had reported sustained rising pressure in its area. Since that part of the North Atlantic often impacts Great Britain's weather patterns, an unexpected narrow window of opportunity had just opened for June 6th.
If the weather held, Allied troops would not have to wait two more weeks (which, it turns out, would have been utterly catastrophic to the outcome of the mission) to attempt the greatest amphibious invasion in history.
They would also avoid the risk that General Erwin Rommel (the German commander who was caught completely unaware in early June) would reposition his troops to better fortify the Normandy coast (just a small part of the "Atlantic Wall" which Hitler and his forces had created for Germany).
At 0415 hours, June 5th, Dr. Stagg briefed Eisenhower and the planning generals one last time. The unseasonable high, first reported by the British ship, would give Allied troops good weather throughout the night and into Tuesday afternoon.
The long-planned, risk-filled invasion would soon become reality.