How does Puck manage to transform Bottom's head into that of a donkey without any of the other actors noticing?
In Act III, Scene 1 of this play, Puck does transform Bottom's head into that of a donkey. But I think you are wrong to say that none of the other actors notice that this change has happened.
First of all, the change itself happens offstage. Bottom speaks a line and then says that he hears a voice. So he exits and is, presumably out of view of the actors. While he is offstage, Puck changes his head.
As soon as he reappears on stage, the other actors do notice the change. They fear that he is a monster and they run away.
So they do notice that the change has happened. They don't actually see the change happen, though, but that is because it takes place offstage.