If you got the choice to change the notification service, instead or directly using firebase, you could use Onesignal which extends firebase and they already have a service named VOIP notifications which should kinda do your needs and here is the link:
https://documentation.onesignal.com/docs/voip-notifications
In case your are restricted with firebase or need to know how this could be done, bellow will be the way to achieve it..
As for android:
First as logic part, you need to add some code in the native layer since hybrid apps usually can't interact from JavaScript side to native side in case app was not launched, so in order to wake the application on a specific event like notification received or any other actions that phone system can hold..
Second, as technical part, you need to add broadcast receivers and the receivers role stand to interact as native code with system. example in the link below:
https://www.digitalocean.com/community/tutorials/android-broadcastreceiver-example-tutorial
also another video about foreground and background broadcast receiver service in the link below:
https://www.youtube.com/watch?v=rlzfcqDlovg
video code output in git:
https://github.com/borntocoderepos/callrecorder
in the Youtube video example, the user is launching a toast message on phone call if app was opened or closed (background or foreground) so you can launch your app with intent with passing data and capture the data on app start as Deep Links as capacitor (https://capacitorjs.com/docs/guides/deep-links) or Cordova (https://ionicframework.com/docs/native/deeplinks)..
And instead of listening to network or phone calls, you can listen to Notifications and for sure you need to do searches about your topic and or the notification service that you'll choose.
Now for the video and the tutorial not sure of the quality of code so make sure to do more researches about the way its done from different places (could be outdated code or bad code quality or even not complete service and will discuss about this point below).
In android there is policy about using background and foreground services so once you start a service you need to end it after your done so make sure after you receive the notification and launch your app to stop the listening since it would cost power usage and perhaps could be stopped by Playstore as harmful app.
Now considering IOS it should be the same concept so make searches about this topic, but for IOS, the listeners policy as I remember , the receivers should not be waked up for more than 15 mins, so also keep this in mind and make sure you stop the receivers directly after launching your Hybrid app.
Broadcast equivalent receiver for IOS:
http://www.andrewcbancroft.com/2014/10/08/fundamentals-of-nsnotificationcenter-in-swift/