My Interstitial Ad not working, does not start

This is simply because you have implemented your if-else wrongly. You are loading ad only when you have interstitial instance, but as your if case is checking wrong condition, you are not going to initialise the instance anyway!

you need to verify the instance just before showing the Ad, not before initialising.

if (mInterstitialAd != null) {
  mInterstitialAd?.show(this)
} else {
  Log.d("TAG", "The interstitial ad wasn't ready yet.")
}

change your code to :

    class MainActivity : AppCompatActivity() {
    
    private var mInterstitialAd: InterstitialAd? = null
    private final var TAG = "MainActivity"
    
    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.activity_main)
    
        MobileAds.initialize(this) {}
        adView?.loadAd(adRequest)
    
            InterstitialAd.load(this, AD_UNIT_ID, adRequest, object : InterstitialAdLoadCallback() {
                override fun onAdFailedToLoad(adError: LoadAdError) {
                    Log.d(TAG, adError.toString())
                    mInterstitialAd = null
                }
    
                override fun onAdLoaded(interstitialAd: InterstitialAd) {
                    Log.d(TAG, "Ad was loaded")
                    mInterstitialAd = interstitialAd
                }
            })
    
            mInterstitialAd?.fullScreenContentCallback = object: FullScreenContentCallback() {
                override fun onAdClicked() {
                    // Called when a click is recorded for an ad.
                    Log.d(TAG, "Ad was clicked.")
                }
    
                override fun onAdDismissedFullScreenContent() {
                    // Called when ad is dismissed.
                    Log.d(TAG, "Ad dismissed fullscreen content.")
                    mInterstitialAd = null
                }
    
                override fun onAdFailedToShowFullScreenContent(p0: AdError) {
                    // Called when ad fails to show.
                    Log.e(TAG, "Ad failed to show fullscreen content.")
                    mInterstitialAd = null
                }
    
                override fun onAdImpression() {
                    // Called when an impression is recorded for an ad.
                    Log.d(TAG, "Ad recorded an impression.")
                }
    
                override fun onAdShowedFullScreenContent() {
                    // Called when ad is shown.
                    Log.d(TAG, "Ad showed fullscreen content.")
                }
            }

        if (mInterstitialAd != null) {
            mInterstitialAd?.show(this)
        } else {
            Log.d("TAG", "The interstitial ad wasn't ready yet.")
        }
    }
    }