Essentially, at the rudimentary level, animals (or people) without language have no symbology to represent things they cannot see.

This is demonstrably untrue in a strict sense.

If I pick up my keys and put on my boots, my pet dog starts running around and panting because he anticipates a walk. He doesn't see a walk, but he has formulated a belief based on abstraction and expectation from prior concrete experiences.

Now you may say that you're using "see" in a broad way--they have to have some sense experience to recall a prior phenomenon (e.g. condition in the vein of Pavlov) and that's probably what you mean, but it's important to note that non-human animals can have abstract beliefs, even if those beliefs are based on prior concrete sense experience.

That having been said, I suppose it's not clear what is meant by "thinking" in the OP's question, as we also know that non-human animals have dreams, which are purely mental fabrications, of course. These thought processes do not require language. And least someone say that they require sense experiences of some kind, we also know that fetal animals dream. It may well be the case that they have some kind of sense experience (I have to admit my ignorance here), but intuitively, I would think that they don't.