Initialize List in User Data Class without deleting binary file

Hi, in my game I save the Data in a binary file using a UserData Class. For the next update I want to add a List of Integers (unlocked Levels), but it doesn't work (nullreferenceexcepetion). I already know the cause: the file already exists but is empty because the List didn't get initialized. This is the UserData. class before the update (excerpt):

 [Serializable]
  public class UserData
  {
      public int score;
 
      public UserData()
      {
      score = 50;
      }
  }

And now I added the new List:

 [Serializable]
  public class UserData
  {
      public int score;
      public List<int> unlockedLevels;
      public UserData()
      {
      score = 50;
      unlockedLevels = new List<int>();
      unlockedLevels.Add(1); //unlocked by default
      }
  }

For saving and loading Data I use my Data Manager Class:

 public static class DataManager
  {
      public static List<int> GetUnlockedLevels()
      {
          UserData userData = Load();
          return userData.unlockedLevels; 
      }
  
      private static void Save(UserData data)
      {
          string path = GetDataFilePath();
          BinaryFormatter binaryFormatter = new BinaryFormatter();
          using (FileStream fileStream = File.Open(path, FileMode.OpenOrCreate))
          {
              binaryFormatter.Serialize(fileStream, data);
          }
      }
  
      private static UserData Load()
      {
          string path = GetDataFilePath();
          if (!File.Exists(path))
          {
              UserData userData = new UserData();
              Save(userData); 
          }
          BinaryFormatter binaryFormatter = new BinaryFormatter();
          using (FileStream fileStream = File.Open(path, FileMode.Open))
          {
              return (UserData)binaryFormatter.Deserialize(fileStream);
          }
      }

In the Unity Editor I could solve issue this by deleting the file and start the game again. However to solve it on the device I think I have to uninstall the app and reinstall it. But this is no solution for me as there are already people owning the app. How can I solve this through code? How can I get the list initialized without deleting the file?