Mercury - I mean for it to be an abduction and no parental involvement. Of course 5.30 would be in line with other theories.
Misty - the window bothers me because realistically you would get max 20mins assuming a 10min buffer on either end in case the checkers deviated from their routine and not much time for misdirection/staging and why bother in this case?. The window would make a reasonable amount of noise in that room and whoever was doing the abduction would be shitting it in case the other children woke. Is the window worth raising if on your own? But with an accomplice it makes more sense to me, but still when the window was raised you would have the noise problem of waking the children. TBH I think if abduction is the case someone opening the window from the outside and coaxing the girl over and then pulling her through makes sense to me...they never entered the apartment... If there were 2 of you - why bother opening the window at all if one of you was already inside? Why not just leave via the front door? Window seems like an unnecessary risk in many scenarios to me...
The open window rules out the woke and wandered theory. So why would an abductor rule himself in
It doesn't make any sense never mind noise, risk incriminating oneself (no glove marks lol), time wasting, window facing the world etc. Why an abductor would open it doesn't make any sense if he didn't enter that way - he could take a child quicker than he could open shutters and window.
A predator is the only other credible explanation and that could connect to a lone Smithman and not a team. You would have to investigate everyone who was on the streets that night e.g. the checkers, Jes, tapas diners and compare them to witness efits to get your first suspects in for questioning but the ones who repeat no comment and hide behind lawyers when the going gets tough should be carefully investigated.