I don't know all the backstory to this, but, really, why would the mother necessarily have staged the window? Isn't it entirely plausible that the abductor came in or out that way? Especially if the abductor was an experienced burglar?
For one thing, it's the closest access to the child, so it's the quickest and surest for snatch and get out, it would take only seconds. It doesn't involve crossing any rooms and potentially being seen if someone is unexpectedly in the apartment. It guarantees you won't run into someone coming in one of the doors. It guarantees someone won't realize anything is wrong until they come into the bedroom. If someone comes in the room and notices the window open, they themselves are unlikely to be able to follow you out the window. They have to take the time to go around and out the door, and by then you're long gone.
Well this is where we get into stuff that is impossible to know unless the Tapas group finally resolves all the contradictions in its evidence.
But we do know it was not the point of ingress because the shutters would have to be broken and there was simply no evidence of it. Instead the patio door was unlocked which neatly explains the lack of evidence of forced entry.
And why leave via the window when you can just walk out either door?
Finally if the shutters were up, and windows open, everyone approaching via the front door had to see this
IMO this is why Gerry finally admitted he never came in the front door