The Apple Store came online at approximately 12:06 AM PDT, and remains up at this time. The Apple Store app on iPhone was online at approximately 12:03 AM, and promptly processed orders from four members of TMO's staff.
Orders placed in the first two minutes were promised between April 24th and May 8th, but my order at 12:06 AM was pushed back to May 13th to May 27th.
Apple Watch Order
We've had numerous reports from readers of similar shipping times for Apple Watch Sport and Apple Watch. Those times are likely to slip further into the future as the morning wears on.