How do I completely reset a game?

You can't do this, also Time.time is the current time which will always go forward. What you can do is making sure to reset everything when you load the start scene. Even for objects marked as DontDestroyOnLoad you have the chance to reset things.

A typical DontDestroyOnLoad object as a singleton:

 public static GameManager instance = null;
 //first code to run
 void Awake()
 {
     //singleton
     if (instance == null)
     {
         instance = this;
     }
     else if (instance != this)
     {
         //singleton, meaning there can only ever be one instance of a GameManager.
         Destroy(gameObject); //<- this makes OnDestroy() be called, be careful
         return;
     }
     //the rest is done once only...
     DontDestroyOnLoad(gameObject);
     //...
 }