This happens on a device with no apps installed, with no apps running. No Apple ID. Fresh install.
Also, locally running apps can trigger their own notifications.
Also, locally running apps can trigger their own notifications.
On a fresh install you have Software Update, News, Safari, iTunes Store, App Store, Stocks, etc. which are all going to be a part of polling for available push notifications. When a new device update releases you will get a notification about it, even without an Apple ID signed in.
Yes, locally running apps can trigger time-based notifications but all network-based notifications should be handled by Apple's push services as iOS doesn't allow long-term persistent background tasks due to battery drain and it doesn't make sense for every app to have its own individual polling occurring at random times.