Arya has spent her entire time on the series training — she was even sneaking her way into the yard to do so in the pilot. She trained with a master swordsman. She survived escaping King's Landing and fending for herself on the road. Later, she shadowed Tywin Lannister. Even later than that, she went to Braavos to become a Faceless Man and survived what should have been a death sentence at the hands of the Waif. She got revenge on Walder Frey for killing her mother and brother by serving him his own family in a pie before killing him. Arya has absolutely earned her place as the one to kill the Night King.