Say you are carrying a girl behind you on your motorbike. She can only look at your back.
If she wants to clearly look at things that are in front of the motorbike, she has to "stick her head out / over".
Another example, these people are standing behind a tree and if they want to see things in front of the tree, they have to "stick their heads out / over" as shown in this picture.
Is it natural to say "she stuck her head out to see the front" or "she stuck her head over to see the front"?