You need to find another way up to the second floor first.
The closet is a great way to get up the second floor.
Did you notice the pegs in the closet?
Try pulling one. The closet is an elevator.
The third peg will take you to the second floor. Pull on it.
Open the door & get out. There's a knob on the staircase.
Turn it. It will click. Now you can walk down the staircase.