I'm afraid it's a little unclear precisely what you want to say, or what kind of sentence you need for the context.
I'm guessing you need either:
1. Searching for the best girl in the world.
2. The search for the best girl in the world.
Both sound like titles of magazine articles. Is that the kind of thing you're after? Anyway, take your pick, because the context is still a little unclear.
It's difficult for me to imagine a context in which I would consider "The searching for the best girl in the world" to be a viable option. It's an example of one of those sentences that would virtually never be uttered by a native speaker, and so I want very much to tell you it's wrong...but I can't because it isn't.
Student or Learner