How can I turn off in-game GeForce Experience notifications?

As of a recent update (somewhere around October 2016), there is a "Notifications" tab in the share overlay settings, where one can turn off this notification.

From the share overlay (opened with Alt+Z) got to Preferences -> Notifications. From there, set "Share your gameplay" to "OFF" and the notification will no longer be displayed when opening games.
The several other notifications from GeForce Experience can be toggled from this menu as well.

I do not know exactly which update introduced this - I can't find it in the version history - but I have version 3.0.7.34 and I am able to switch off the notification.

There's a share button on the General page, disable sharing and you disable the notifications. Of course if you want to record game play or broadcast on Twitch you'll have to turn it back on again. I know, not really a solution, but I prefer turning on and off sharing, which is just fast click of a button, when I record, instead of having to continually see those notifications. I couldn't find any other way to do it.