Well, if Engine.has_Singletom("Admob") returns false, I have a couple questions.
First, check in your Project Settings. There's a section for Android. Do you have
org/godotengine/godot/GodotAdMob in the Modules list?
Also, check through the hidden files of your game. There should be a folder labeled "android". In the "build" folder within that, you should have your "admob-lib". Is it in there?