Has to be a camera trick doesn’t it? The camera freezes at about 31sec which could hide an edit. He puts the card on the glass at an angle but it’s perfectly straight and aligned with the window frames afterwards? Or maybe all the reflections on the glass hid a mirrored sticker that he just peeled off to reveal the already placed card.
There is something odd about the physics of the card on the orangutan side. It seems to float as he pulls it away from the window initially- perhaps fishing line? The other thing that I think might be illuminating is the tapping of the stick on the card as if he is trying to reapply it- could this be imitating something he watched.
Those both being said, I like Mavic Chen’s suggestion of a mirror and reflection hiding an already placed card.
I like the peel off mirror theory too. The hard part would be getting the card into the orangutan’s enclosure. They can be dangerous animals. Fishing line seems like a plausible solution.