Pulling Out First Tooth...

My niece is 6 years old and she has her first loose tooth. There's even a tooth growing behind it!! She's petrified of letting anyone go near her tooth but it has to come out. I have her for the week and would like to get this tooth out. How can I get her to let me try to pull it. She starts crying anytime we talk about it

Let her bite into an apple.
Give it some time, when I was little I didnt even tell my Mom it was loose I just played with it and pulled at it until it came loose.
If anything take her to the dentist or just let nature take its course