After installation the user will probably start or setup your app. You could add your own webhook notification when the user goes through this First Run Experience. (This is what we did)
There is another thing you might be able to pull off: As far as i know, an event is fired to Google Analytics on install. Maybe you can add an alert/webhook in Google Analytics.
However, i was having some problems with the events to show up in GA in the first place.
You can use the license notification api to retrieve a list of current installs. https://developers.google.com/apps-marketplace/v2/reference/licenseNotification/list
After installation the user will probably start or setup your app. You could add your own webhook notification when the user goes through this First Run Experience. (This is what we did)
There is another thing you might be able to pull off: As far as i know, an event is fired to Google Analytics on install. Maybe you can add an alert/webhook in Google Analytics. However, i was having some problems with the events to show up in GA in the first place.