If you have not configured one of the following rules
- Maximum number of check attempts for Hosts|Services
- delay host|service notifications
- Notified Events for Hosts|Services
the notification should be instantly created and be be visible in the analysis in setup - notifications.
What is “Service Notifications” of that service showing after the event when you click on the affected service and is there a “Notification postponement reason” in the table of that service ?