According to the description you gave you need to use Push API instead of just Notifications API. Think about the API
Push as a Notifications with "steroids".
Whether your site is static or dynamic this API
is javascript
and runs on the user’s browser, however it is a little more laborious to implement than the Notifiuncles.
This API
is available in Service Worker and needs a back-end as a service to actually send notifications to the customer (user).
There is a large offer of services (servers) that make this work of back-end for Push free or paid that may even have good documentation for you to implement a Service Worker on your website however if you own a server (manage) it might be a good idea to implement your own service and maintain full control over the notification system.
I usually don’t like posting answers like: "follow this link here" but if I were to post the codes to implement Push with due clarification would be a very long post beyond what is not needed "reinvent the wheel" with such a large range of good materials and good sources.
Then follow the links:
Service Worker:
Push API:
The example of the site Google Developers is very good but does not teach to create a service itself if you are interested in diving head first you can start by taking a look at the list of libs hosted on Github i particularly recommend web-push made to run on Node.
editing:
A Cookie Book about Push API (maybe the best I’ve ever read)
Are you using wordpress? the Onesignal Plugin does this for you. Doesn’t it answer? try looking for something like Web Push Notifications.
– Bruno Folle