How do cats implicitly know how to use the litter box?

You've got it backwards. We didn't teach them to use the box, we created an artificial area that mimics the environment they prefer to poop in.

E: typos

You’ve generated a synthetic reality for your cat. His life is a lie.
- His life may be a lie but the poop is very real.
- Unlike the cake

Poop smells.

Small non communal prey animals want to bury it so predators don't find them.

Ambush predators like cats want to bury it so prey doesn't smell it.

Herd prey don't hide it because they're not hiding from anyone. And pack hunters like wolves don't for the same reason.

So modern cats want to hide it instinctually. Their urine as well because just the tiniest hint of cat piss is enough for mice to flee a property.

Meanwhile, my dog: it's raining outside so I guess I'll just take a shit on the deck.
- Got excited, better piss on the couch
- Yours needs rain to do this?
- Also, I'm going to bury it. Yes I know previous poster said us pack animals don't do that but who gives a shit I am not part of your system. I also know this deck is built out of solid wood planks so of course I am not actually burying anything, I'm just scratching up your deck really badly. But this I will do and nothing can stop me.
I've got cats that are so desperate to bury their urine/feces that they will dig and scrape at whatever is around to do so, including the wooden floor. We noticed this when we'd empty the litter box into a bag and leave the bag by the door to take to the bin. If a cat found the bag they'd immediately start scraping at anything around to try to bury it, no doubt because of the scent.
- Yeah, that's pretty typical. Every cat I've ever known has done the same thing. Not just poop though, anything smelly must be buried.
Small non communal prey animals want to bury it so predators don't find them.
Their urine as well because just the tiniest hint of cat piss is enough for mice to flee a property.
Then why do I have mice in my walls?
- Do you have a cat?
  Start buying unscented litter

They don't. You have to put the kitten in the box. The boxes and litter are designed to meet their natural preferences of being able to hide themselves and their excretions, so sticking the kitten in the box a few times is usually enough for them to recognize it as a safe place to go.

They're going to go somewhere and when they do you put it in the box.
- Just put it in the box
You dont essentailly have to. They try to find the most optimal place to do thei business when they have to. Assuming your kittens are only at 1 room at first they dont have much trouble finding it. Of course some cats can be bit stupid and you have to actually show them that it excists

The other answers are correct but they also copy their mums once they’re old enough. I’m in the UK where it’s the norm to let your cats outdoors. When my neighbour’s kitten was old enough to be let out he used to follow my much older cat around and copy her. He watched my cat do a wee in the bushes and then copied her digging to cover it up. Just covering up his imaginary wee next to her! It was super cute, although my cat wasn’t that impressed with the intrusion.

Cats are desert animals. Them going to bathroom in the sand was always a thing.

What about all the jungle cats?
- Jungle sand. There is a wide variety of sands; jungle sands, desert sands, pocket sands, beach sands, etc.
- https://www.wildcatfamily.com/felidae-evolution/
- They have camo litter boxes

Cats are both prey and predator and evolved to hide signs of themselves. They naturally want to cover up their urine and feces so that a larger predator can't track them. We brought them inside the house, but that hard wired behavior still exists.

To hide their scent from predators.