Objects can indeed appear to us without necessarily having to be related to functions of the understanding. (A89/B122)
Appearances can certainly be given in intuition without functions of the understanding. (A90/B122)
Appearances might very well be so constituted that the understanding would not find them in accordance with the conditions of its unity…. [and] in the series of appearances nothing would present itself that would yield a rule of synthesis and so correspond to the concept of cause and effect, so that this concept would be entirely empty, null, and meaningless. Appearances would none the less present objects to our intuition, since intuition by no means requires the functions of thought. (A90–91/B122–123)
How is Kant here justifying the proposition that there do exist intuitions without understanding?
For example, we may consider a dream, from which when we wake up we realise it was not real because the unity of all categories needs to be preserved by experience. However, even inside the dream, I think of permanent substances and cause-and-effects applied to appearances. It just so happens that later this gets 'destroyed' by another cognition (in this case, waking up). I can simply say that I considered the dream as a 'dream' just to fit the narrative to preserve my Unity. Nevertheless, Kant has still not given an example of pure appearances, i.e, intuitions where concepts have not been applied by us.
Moreover, if he cannot do that, why does he have this distinction between understanding and intuition at all?