You can have a Delayed Linedef Executor at the beginning of the level.
Or if you want to do it the lazy baby's way, a Gargoyle Box.
...You sure you don't have that isn't the other way around?
EDIT: Then again...
If you just have the Executor start moving a floor down (With the Gargoyle on top, of course) and lower it into an intangible FOF and time it, you can easily do the same without the need of an ENTIRE box, so... Yeah.
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