if u play enough u can do it with the feet open door and comming trough i did it so ^^ but u can also "cheat" a bit with the reset stuff u always Reset where youre feet is so if u place them under the button just reset and Spam E to open and if u opened it then just try to get the feet in the stairs and use also again Reset the u land into the room with the stairs and you are save ^.^
(i read it so that u didnt clear it if so just ignore then my post :P )