When in the life of a ticket is the first reply time recorded?
In reporting, the first reply time metric is calculated by measuring the time between the customer's first message on a ticket and the agent's following public reply. This applies to tickets created by the requester, but also to tickets created on behalf of the requester, by an agent.
In a ticket created by the requester emailing support directly, first reply time is calculated as the time between the requester's comment when the ticket was created, and the first public reply on the ticket from an agent.
In a public ticket created by the agent, on behalf of the requester, the first reply time is calculated as the time between the proactive message and the agent's next public comment on the ticket.
For more information, see this article: Understanding first reply time.