This is highly dependent on what version of Firebase SDK you use.

 pubspec.yaml

simple_firebase\pubspec.yaml

dependencies:
  flutter:
    sdk: flutter
  firebase_core: "^0.5.0"

  # Add the dependency for the FlutterFire plugin for Google Analytics
  firebase_analytics: ^6.0.0

  # Add the dependencies for any other Firebase products you want to use in your app
  # For example, to use Firebase Authentication and Cloud Firestore
  #firebase_auth: ^0.18.0+1
  cloud_firestore: ^0.14.0+2

android\gradle\wrapper\gradle-wrapper.properties

Change

#distributionUrl=https\://services.gradle.org/distributions/gradle-5.6.2-all.zip
distributionUrl=https\://services.gradle.org/distributions/gradle-6.3-all.zip

Or you will may this error later

Could not initialize class org.codehaus.groovy.reflection.ReflectionCache

Edit both the project and app build gradles

simple_firebase\android\build.gradle

 dependencies {
        classpath 'com.android.tools.build:gradle:3.5.0'
        classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlin_version"
        // Add the following line:
        classpath 'com.google.gms:google-services:4.3.3'  // Google Services plugin
    }

simple_firebase\android\app\build.gradle

Add the following

apply plugin: 'com.android.application'
apply plugin: 'kotlin-android'
apply from: "$flutterRoot/packages/flutter_tools/gradle/flutter.gradle"
//Add the following line
apply plugin: 'com.google.gms.google-services'  // Google Services plugin

Update you minSDK

defaultConfig {
        // TODO: Specify your own unique Application ID (https://developer.android.com/studio/build/application-id.html).
        applicationId "com.example.simple_firebase"
        #minSdkVersion 16
        minSdkVersion 21
        targetSdkVersion 28
        versionCode flutterVersionCode.toInteger()
        versionName flutterVersionName
    }

Remember you applicationID because you will need it when you register your app with Firebase

Register app with Firebase

Add google-services.json

simple_firebase\android\app\google-services.json

OF you will get the folliwing error File google-services.json is missing. The Google Services Plugin cannot function without it.

Commands

./gradlew build