One option is to use the Genesys AWS Event Bridge integration:
You can then listen for v2.detail.events.conversation.{id}.acd.end which fires when an agent picks up a conversation or if the customer hangs up or gets transferred out of queue by something (normally the IVR). So you will have to look into the contents of the message to sort out if this is an event that you care about. I don't know exactly what to look for here.
You could then process that event in AWS (probably a lambda) to determine if you should send a notification to your other system.
Eventually I would hope that our Process Automation Triggers could do this for you without the need for code, however I don't think we have everything in place for your use case yet.
Taking an action when an agent answers an ACD routed conversation seems like a common use case. If you agree, please submit an idea to have a specific "ACD conversation answered" topic: https://genesyscloud.ideas.aha.io/ideas