XEP-0203: Delayed Delivery is usually attached to messages, when they are sent from the server's offline storage.
Checking if a message has delayed delivery info attached is pretty simple:
DelayedDelivery delayedDelivery = message.getExtension(DelayedDelivery.class);
if (delayedDelivery != null) {
// This message was sent from offline storage
}
There's also a convenient method to retrieve the send date of a stanza, which is either “now” (real-time) or some time ago in case the server stored the stanza for delayed delivery, e.g. in an offline storage:
Instant sendDate = DelayedDelivery.sendDate(message);