Web Messaging SDK: Push notification to guest with closed session

Trying to send a proactive push notification to a guest who had a web messaging session yesterday. The session is closed, so sendNotification on the active widget instance throws a 403. I have the conversationId and contactId from our DB. Is there a specific API endpoint or SDK method to target a specific contact for a push alert outside of an active session? Or do I need to re-initiate the widget?