Looks like they are starting to ship. AT&T has begun sending out emails.
Dear Valued AT&T Customer,
Thank you for ordering the Samsung Galaxy SŪ 4 from AT&T. We are excited to announce that we are able to ship devices earlier than originally expected. Customers who preordered their smartphone early can begin receiving it as soon as April 25th.
You should expect to receive an Order Confirmation email with your shipment tracking number as soon as your order has been shipped.
AT&T is committed to outstanding customer service and we hope you are as delighted with this good news as we are to be sharing it with you.