You can develop push notifications using the Google developers guide. But, building your web push could be a time taking process.
You can use free push notification providers like Truepush to send unlimited push alerts to your users. This would save your time, resources, and hefty dollars you could spend on re-engaging your users.
If you have a PWA powered website, you can follow the guide for sending PWA push notifications.
For AMP powered websites, read the guide for sending AMP push notifications.
For a direct WordPress plugin, check the integration guide here.