We don't have access to "what is there". What we have are sensory experiences.

So we know that whatever is there must include those sensory experiences. They themselves are part of reality.

But the model isn't supposed to look like our experience it is supposed to predict it.

Most models of reality are partial models that implicitly presuppose some untheorized notion of experience in the model-user. Medicine and engineering aren't especially focused on the fact that doctors and engineers encounter the world, like everyone else, through the medium of conscious experience.

But there are two types of explanatory enterprise where conscious experience does become explicitly relevant. One is any theory of everything. The other is any science which does take experience as its subject matter. In the latter case, scientists will explicitly theorize about the nature of experience and its relationship to other things. In the former case, a theory of everything must take a stand on everything, including consciousness, even if only to say "it's made of atoms, like everything else".

So some part of these models is supposed to look like experience. However, as I have been saying elsewhere, nothing in physical ontology looks like an experience; and the sciences of consciousness so far just construct correlations between "physics" (i.e. matter) and experience. But they must eventually address the question of what an experience is.