sample.cs

public class PageNavigationManager
{
  public static PageNavigationManager Instance { get; } = new PageNavigationManager();
  
  private INavigation Navigation { get; set; }
  
  private Dictionary<string, Type> PageMap { get; } = new Dictionary<string, Type>();
  
  public void Init(INavigation navigation)
  {
    this.Navigation = navigation;
  }
  
  public Task NavigateAsync(string pageName)
  {
    return this.Navigation.PushAsync(Activator.CreateInstance(Type.GetType(this.PageMap[pageName])));
  }
  
  public void RegisterPage(string pageName, Type pageType)
  {
    this.PageMap[pageName] = pageType;
  }
}

// usage
// ページに来たときあたりに初期化
PageNavigationManager.Instance.Init(this.Navigation);

// アプリの初期化あたりでページの登録
PageNavigationManager.Instance.RegisterPage("HogePage", typeof(HogePage));
PageNavigationManager.Instance.RegisterPage("FugaPage", typeof(FugaPage));

// 画面遷移
await PageNavigationManager.Instance.NavigateAsync("HogePage");