If your goal is to send an alert notification only after it has been firing for some time, the usual way of doing that in Prometheus would be to use the "for" duration field in the alerting rule to define how long the alert has to be active before it transitions from "pending" into "firing" state (at which point it gets sent to AM and routed there).
If you do want to route it before that duration already, but to a different subtree / notifier in your AM routes, you could define the alerting rule twice in Prometheus with differentiating labels and different "for" durations.