Finding date when message was sent by Service Broker

The sys.conversation_endpoints table has a lifetime column. You can use that to determine the time when a conversation was started as follows.

SELECT DATEADD(SECOND, -2147483647, lifetime) FROM sys.conversation_endpoints e
WHERE e.conversation_id in ('CAAB52B9-C6B3-4DD8-9E1F-7C0CD93D7724', '7AD93224-3700-4054-9BD2-7B52C9430C17')