Usually imagination is considered as ultimately subjective thing, that what is imagined doesn’t belong to the world, but exists just as some purely mental-thing.
But on other side imagination as the other mental acts shows as being towards transcendental objects – We can imagine same thing multiple times, or we can talk with other person about the same imaginary thing.
So what is imagined can’t be fully subjective.
To figure out how this can be, we might think of situations where the children are encountering (their) imagination, and in which might notice it as specific mental act (of imagination). I can think of few such scenarios possible in early years. Of course the list is not in any way systematic…
Expectation… this is the earliest type of imagination I can imagine (no pun intended)…
I see it in really early ages of kids, and makes it possible to
make them laugh doing silly things, like crouching behind the couch
hiding from their view, and then jumping. I guess they laugh at my
stupidity doing such meaningless acts. Expectation doesn’t require language. Of course, sometimes they want you to repeat the act, so they make some sounds… until you do it again… And again… And again… They are never satisfied. In the expectation, they see more in the situation then there is “physically“. E.g. they expect the jump – they wait for it. There in front of them, in the world.
Playing with toys… Seeing in the toys more then there is (physically). Pushing toy cars around, also hitting the ball. Those things are seen as part of the potential of the thing, the ball is hittable, the toy-car is pushable, etc.. This possibilities are there in the toys for the kid. This also doesn’t require language.
Stories… about what has happened, really or not. To me, to Little Red Riding Hood, or to Harry Potter. This is as much about imagination as about language. Hard to divide. Language is not possible without imagination it seems, and stories without language. But in any case, the person who tells the story is in the world, and the words are in the world, the Little Red Riding Hood is also imagined in the world… noticing, moving, talking. Where can she watch, move, talk if not while (imagined as) being-in-the-world.
Promises… about what will happen. To the kid if he does his homework. Or that he can play on the computer tomorrow. Again, not possible without language. Surely connected to expectations. They are also about the world. They happen or don’t in the world.