Creating instance at the beginning of the game

How can someone create an instance at the beginning of a game? ... what I am doing now is basicly this

 public static class MyClass
 {
     static private MyClassCleaner = (new GameObject "MyClassCleaner")).AddComponent< MyClassCleaner> ();
 
     static public Cleanup()
     {
         //Cleanup code
     }
 }
 
 public MyClassCleaner : MonoBehavior
 {
     void Awake()
     {
         DontDestroyOnLoad(gameObject);
     }
     public void OnDisable()
     {
         MyClass.Cleanup();
     }
 
 }

But this doesn't create the GameObject. I wanted the code above to create a persistent gameobject that cleans up my MyClass static class at the beginning of each level. Is there a way to create a GameObject at the beginning of the game?

Is there a way to do this using static methods or by coding or is the only way creating a game object and attaching the MyClassCleaner script to it?