alertmanager the alerting component of prometheus. So how long can it take between an event happening and you getting notified about it? Since they're both written by the same team, they work more or less the same way: timer based event loops.
So what triggers things to happen?
In the most unfortunate case:
$scrape_intervalto get the initial data
$evaluation_intervalto check if alert is firing
$for(round up to nearest
$evaluation_interval) to trigger the alert
$group_waitto send initial notification
Now say you have another on call system layered on top. It too is likely to be evaluation_interval / delay based, so your total delay is even longer....