If that's a requirement, I would add a custom status, for instance New Ticket. Configure new tickets to use this status whenever they are opened.
Your escalation looks for this status, sends the response, and sets the status to something else, like Waiting For Support. Then the response will not fire again unless the ticket status is changed back to New Ticket.
I have a fairly similar escalation where I have new tickets come in with the New Ticket status. When a moderator claims a ticket, they set the status to Waiting For Support. If they make a change (e.g. trigger a password reset), they can change the status to Waiting For Customer. An escalation is in place to say that if the status is Waiting For Support and the last reply was the ticket opener, change the ticket back to Waiting For Support.