It seems to be a big deal that we see things as they are. If we are merely assuming when things begin and end or change then how do we ever really see things as they are?
From Mahayana perspective "things" do not "end", nor do they "change" - because separate self-identical things are imputations of the mind. In reality things do not have firm spatial and temporal boundaries. Things do not by themselves have identities that stay unchanged throughout their lifecycle, allowing us to designate it as "still the same thing, just changed a little". These identities are chosen by us. So to speak of any "thing", "ending", "changing but still staying itself" - is a simplification. Ontological reality has nothing like that, it is totally up to observers to define "things" in space and time.
How do we "see things as they are" then? We see them with our "wisdom eye" (wink wink).
We remind to ourselves that what we see is not all there's to it, until we are used to seeing it all. For a trivial example, when someone dies, we say: it only looks like this person ended, but that is not true - there are children, books, students, flowers, social influence - whatever imprints they left on the world - it lives on.
When we practice this enough we get in the habit of seeing "energies", "influences", "connections", "processes" behind things. We no longer see separate things, we see the matrix - and that's called "seeing things as they are".
From Mahayana perspective, this is the real nature of Impermanence: everything is continuously in flux, but the mind grasps after "entities" that it itself designates, and then gets upset when these imputed entities morph beyond recognition, like the cloud figures.
It seems to be a big deal that we see things as they are.
When we say, 'to see things as they are' in Buddhist context, we mean to see things not clouded by ignorance, for e.g, when you see a beautiful women, you really only see a beautiful women...because at that moment your perception is clouded by desire and lust...you dont really see her as she is, for e.g. the father or brother of same women will see her differently. That is why the Buddha gave us the meditation on bodily parts...so yes its a really big deal to see things as they are...
If we are merely assuming when things begin and end or change
No, we are not merely assuming the begining or end or change...according to the second law if thermodynamics there is a perpetual change of entropy of the universe. Everything is in a constant state of flux, the sub-atomic particles inside the atoms are moving, the atoms inside things are moving and all things are slowly or otherwise undergoing molecular disintegration. Annicha is a universal law.
The begining of things is not disernable and nor is the end. Change is discernable if you are sensitive enough, aware enough, meditative enough.
then how do we ever really see things as they are?
We ever really see things as they are when we get rid of the three poisions of ignorance, greed and lust. In other words by being more aware to the present moment. By following the eight fold path you gain the wisdom, then you see things as they are.
I guess the concept of emptiness makes that a meaningless question.
If a thing isn't even itself (its own thing) to begin with, how could it stop being that or change?
Maybe you can't identify what you're talking about: a thing, an element of a thing, a contact with an element, an experience of a contact, a description of an experience, etc.: "turtles all the way down".
It might be worth remembering "the purpose" of the doctrine about "really seeing things as they are" -- Kimattha Sutta: What is the Purpose? (AN 11.1) -- here's an extract:
And what is the purpose of concentration? What is its reward?"
"Concentration has knowledge & vision of things as they actually are as its purpose, knowledge & vision of things as they actually are as its reward."
"And what is the purpose of knowledge & vision of things as they actually are? What is its reward?"
"Knowledge & vision of things as they actually are has disenchantment as its purpose, disenchantment as its reward."
If a doctrine is something like, "Gold is forever", that might have a result -- like lust and craving (for gold), attachment.
If a doctrine is something like, "You can't take it with you", that might have a different result -- detachment, dispassion, etc.
Other suttas use the term to describe the knowledge and vision of someone who is without fetters.
Also people sometimes express an opposite take on it -- i.e. that there's No coming and no going.