I want to push notification to users when in my beacon's proximity. That's pretty easy if I register my beacon on Google Beacon Platform using Proximity Beacon API and then register Nearby Notification against it. I do not want to register the beacon on Google Beacon Platform and still throw a notification to user through Nearby Notification API.
If you want to Google Nearby to be triggered by a beacon, you have no choice but to register the beacon with the Google Beacon Platform. That's how it works. Nearby is a system that relies on server-side configuration to send messages to a user.
That said, it is possible to send regular Android notifications to a user when they come across your beacon without registering with the Google Beacon Platform. To do this, you must have your own custom app installed on the user's phone.
You can see an example of how to do this with the Android Beacon Library in the "Getting Notified When Beacons Appear in the Area" section of this page. A more sophisticated example that scans in the background and sends a notification to the lock screen on beacon detection is in the library's reference app.