I have added AdMob advertising in my Android app .
I connected to the AdMob site using this link:
https://firebase.google.com/docs/admob/android/quick-start
Yes, you can use AdMob standalone, without Firebase. But I recommend to implement AdMob using Firebase. It will save you from lot of setup efforts and is simple to integrate in app.
For official site:
Firebase is recommended, but optional.
The best way to use AdMob is with Firebase, but for those publishers who aren't ready to make the switch just yet, Google Mobile Ads will remain available as a standalone SDK. Android publishers can continue to import the play-services-ads Gradle artifact without using the Firebase plugin.