“This antiquated vertical transport machine is faster than stairs but slower than a transmat.”
Head into the elevator in the middle. Once inside, the door will close behind you. Some good dialogue goes between Ghost and Cayde-6 about the elevator itself. Makes you question just what Cayde is doing. It just a short while to get to the top. Once there, you have more climbing to do. Because of the Taken being aggressive against the Fallen, you will encounter a wrinkle in Cayde's plan.