"My problem is that when outage is alerted, it feels waste of time to create a JIRA ticket first"
That is of course easily solved, most alert systems can raise several alerts at the same time and one of those alerts can be the automatic creation of a Jira ticket.
Part of closing that Jira ticket can then be the administrative task of recording (in whatever way/system is suitable for you) what you agree upon as the repair time.
(Already implied but let me state that explicitly: the ticket resolution time tracked by your ticketing system is not the same as the time-to-repair.)
When ticket resolution times are important and a performance metric themselves, you may want close that automatically generated ticket for the outage immediately after the outage has been resolved.
When you start a root-cause analysis (RCA) investigation use a related but new problem investigation ticket #XYZ (which has different performance criteria and gets reported on differently than tickets regarding outages.).
Depending on the RCA outcomes you may start work on a permanent fix / mitigation measures that you track in a different way again, depending on what needs to be done.