Send local push notifications for Android PWA without Cordova Plugin

If I understand you well, yes! you can.

How? By using the native Push API with Notification API. Mozilla and Google have great documentation for them.

You need to check the docs of each plugin you are using, to see if they support the browser platform.

As far as your requirement looks you can use use phonegap-plugin-push which also support browser platform.

Reference:

1. https://github.com/phonegap/phonegap-plugin-push/blob/master/docs/PLATFORM_SUPPORT.md

2. https://github.com/phonegap/phonegap-roadmap/issues/180

Another Solution: Ionic Framework with Push Notifications