singleton.cs

using UnityEngine;

public class GameInstance {
  // Core Game Module
  private Player.Controller _playerController;
  public Player.Controller PlayerController {
    retrun _playerController;
  }
  
  public GameInstance() {
   // ... 
  }
  
  public Init() {
    if(_playerController == null) {
      _playerController = new Player.Controller();
    }
    
    // etc ...
  }
}

// Attach to GameObject in each scene
public class GameManager : MonoBehavior {
  private static GameInstance _instance;
  public static GameInstance Instance {
    get {
      if (_instance == null) {
        _instance = new GameInstance();
      }
      
      return _instance;
    }
  }
  
  void Start() {
    Instance.Init(); 
  }
}

singleton2.cs

public class GameManger {
  private GameManager() {
    // ...
  }
  
  private static GameManager _instance;
  
  public static GameManager Instance() {
    if (_instance == null) {
      _instance = new GameManager();
    }
    
    return _instance;
  }
}