What about the service elevator?
Yes, the service elevator is another option.
The floor plan that I have seen shows that the Mandalay Bay has three wings that each protrude from a center core.
The guest elevators are located in the center core. It looks like at the far end of each wing there is an emergency stairwell. I don’t know where the service elevator is.
Paddock’s suite was at the end of one of the wings, very close to a stairwell. So it would appear that that would be the closest exit to his room.
I have also seen speculation that the stairwell may have provided access to the Four Seasons, which occupies the top floors of the hotel.
I have read speculation that it was possible that Paddock or others planned to escape from the suite by going up rather than down.