So knowing when Kate did her check is the important item.
I would say plenty have tried to work that out before.
Gosh what a difficult topic but one thing is for certain all the Tapas 9 say Kate's check and alarm was after 10:00 PM whereas the OC reception and other staff indicate something happening from 9:15 PM onward. I have not yet discovered what vital fact will determine the true time.
I can see one simple solution - the two incident hypothesis. We know that at 9:15 while Gerry is talking to Jez, Jane sees a person carrying an unconscious child past the OC apartments. Was this Madeleine or someone else, this is the real question.
Could this be the start of the girl's father reporting a child missing, but as can be seen she wasn't missing for someone had her, and hence this person could have been located real quick and hence no need to invoke the OC missing child procedures for the first incident. We have a sighting and reports of an incident, clearly distinct from the MM missing alert at 10:00. What more do we need?