That's a frustrating spot to be in, especially when you're counting on those escalations. I've seen a few teams run into that same "no response" evaluation, and it often comes down to how the system interprets a notification being sent vs. a notification being received or acted on.
One angle to check that hasn't been mentioned yet is the alert's "priority" and the specific notification rules for the primary. Sometimes the initial alert goes out via a channel they've muted or set to low-priority, so from their perspective it's missed, but Opsgenie sees it as "delivered." Then the escalation logic might not even start because the system thinks step one was technically completed.
Have you looked at the notification rules for the primary on-call person to see if there are any filters or overrides that could be quietly blocking the first ping?
Keep it civil, keep it real.