She could have hid in the tree, and leapt out (ie not jumped from above). The generals were quick to see it, and perhaps the crowd surrounding the NK were less generals and white walkers but just more mindless zombies like the one they kidnapped? Those would have been slower off the mark.
The incident may have planned out as follows:.
-Arya knows her purpose, exits the room
-Chaos is occurring by the tree as Theon and his men are firing at walkers
-during that chaos she manages to creep unnoticed into the tree (plausible)
-NK comes in, she leaps out at the right time
-generals can sense it even though they are busy ambushing the castle mostly. But the generals a circling the tree (if any) take notice. Remember there was a fair radius around bran, so it's not like they had no space to cover to get to her in time.
-generals presumably have less skill than the NK so they can't throw a knife from long range to hit her.
-arya leaps to the NK. NK is too clever for the trick and grabs her neck
- ultimately NK takes her for a pawn and underestimates her ability to combat. She does the same trick she used on Brienne and changes hands to the fatal stab.
I think that's perfectly plausible to be honest.
Or she used that Oyster Card she saved up for a few seasons ago, caught the Nothern Line there and actually jumped from the underground?