Why is there even a way to the end of suffering?

MN 64 actually transport the matter that certain circumstances and quoting out of the whole wheels context doesn't make sense at all and would add just a further confused person into the reign here. It's therefore amazing that there isn't a way out of the cause of avijja, improper attention, as long not meeting the outwardly cause of vijja: association with Kalayanamitta.

It had been taught by the Sublime Buddha of what is the cause, what's the way, that someone gains inside by oneself, so it's not understandable how a person, presenting a notion of firm conviction, answers, does, 'smarter' then his teacher and picks out phrases to lead people into common householder-equanimity...

So to leave also an access open, good householder, just that much: "...To what extent is there an awakening to the truth? To what extent does one awaken to the truth? We ask Master Gotama about awakening to the truth.”...Into the Stream.

Much success in trying to leave home and gain a footing in a borderland.

It's the order of nature to go along with craving according to Iti 109. And as quoted by OyaMist, even a little baby has this underlying tendency to go with craving according to MN 64.

However, Gautama Buddha, like previous Buddhas before him, strove and discovered the Four Noble Truths and the Noble Eightfold Path that leads to the permanent end of suffering, and he taught us this with his extraordinary skill of teaching as a sammasambuddha. To discover this on one's own without guidance from the Buddha is extremely rare and difficult, though not impossible.

The Noble Eightfold Path involves going against the order of nature, going against the current. Craving is going with the natural current, and leads to becoming stuck in suffering. Renunciation is going against the natural current and leads to liberation from suffering.

Why is there even a way to the end of suffering?

Well, Edward Jenner discovered the vaccine in 1796, and went against the flow of nature to train the body to fight an infectious disease before it encounters it. This lead to the eradication of many infectious diseases. Otherwise, to suffer from the infectious disease, and possibly recovering or dying, is going with the flow of nature.

Similarly, Gautama Buddha discovered the Noble Eightfold Path in approximately 525 BCE, and that's why we have such a thing today. The noble Right View as taught by the Buddha is the vaccine against permanent suffering.

"Suppose, bhikkhus, a man was being borne along by the current of a river that seemed pleasant and agreeable. But upon seeing him, a keen-sighted man standing on the bank would call out to him: 'Hey, good man! Although you are being borne along by the current of a river that seems pleasant and agreeable, lower down there is a pool with turbulent waves and swirling eddies, with monsters and demons. On reaching that pool you will die or suffer close to death.' Then, bhikkhus, upon hearing the words of that person, that man would struggle against the current with hands and feet.

"I have made use of this simile, bhikkhus, to illustrate the meaning. And this is the meaning here: 'The current of the river' is a synonym for craving. 'Seeming pleasant and agreeable' is a synonym for the six internal sense-bases. 'The pool lower down' is a synonym for the five lower fetters. 'Turbulent waves' is a synonym for anger and frustration. 'Swirling eddies' is a synonym for the five strands of sensual pleasure. 'Monsters and demons' is a synonym for womenfolk. 'Against the current' is a synonym for renunciation. 'Struggling with hands and feet' is a synonym for instigating energy. 'The keen-sighted man standing on the bank' is a synonym for the Tathagata, the Arahant, the Fully Enlightened One."
Iti 109

There's a confusion here between pain (or pleasure) and suffering that goes to the heart of Buddhist teachings. Yes, if I hit my thumb with a hammer I will feel pain, and that has value in teaching me to be more present and cautious when I'm hammering things. But that isn't suffering. Suffering is a purely mental phenomenon: suffering is when my mind becomes so focused on the memory or avoidance of that thumb-pain that I develop anxiety about using hammers, or anger at the hammer for having hurt my thumb, or resentment of the person who told me I should use the hammer in the first place.

Pain is an event that happens at certain (hopefully infrequent) moments of our lives. Suffering is an ongoing mental infliction that can fill all the moments in-between.

Pleasure is also an event that happens at certain moments of our lives, and we can suffer over pleasure just as easily. We experience something we like, and then we find we can't stop thinking about it, can't stop chasing after it, can't stop indulging in it, come hell or high water. We become like a dog who fixates on a ball and charges after it, completely oblivious to the things and people it knocks over in the pursuit, and terribly anxious and frustrated if it finds it can't reach it.

Nothing in the Buddhist worldview suggests that we can or should stop feeling moments of pain or pleasure. That is, as you say, how the world turns. Buddhism teaches that we can stop suffering over those moment of pain and pleasure; break that dog-mind fixation on chasing or escaping. Pain and pleasure are facts of existence; suffering is, well... a lifestyle choice, maybe? And we can choose a different lifestyle.

What Buddha calls 'dukkha' (suffering, dis-harmony) comes from childish, primitive thinking (and action based on such thinking).

As you said, we observe interactions, we figure out patterns and regularities, and based on these we make assumptions about the world.

Problem is, our observations are quite superficial, our patterns are overgeneralized, and on top of that we confuse our observations and assumptions with reality. Then, when the actual reality knocks on the door, we resist and keep on grasping to our ideas. That's what I call "childish thinking" and this is essentially where dukkha comes from.

So dukkha comes from a low skill level, but a skill is something that can be developed. This is why there's a way to the end of suffering, because childish thinking can be outgrown.

Just like people realized that bacteria thrives on bad hygiene - and learned to wash hands - in the same way we can understand how childish thinking leads to trouble and disharmony, and learn to operate on a different level of skill.

This is why it's called The Way of The Civilized ("Arya" in Pali).

Kusala Sutta: Skillful

"Abandon what is unskillful, monks. It is possible to abandon what is unskillful. If it were not possible to abandon what is unskillful, I would not say to you, 'Abandon what is unskillful.' But because it is possible to abandon what is unskillful, I say to you, 'Abandon what is unskillful.' If this abandoning of what is unskillful were conducive to harm and pain, I would not say to you, 'Abandon what is unskillful.' But because this abandoning of what is unskillful is conducive to benefit and pleasure, I say to you, 'Abandon what is unskillful.'

"Develop what is skillful, monks. It is possible to develop what is skillful. If it were not possible to develop what is skillful, I would not say to you, 'Develop what is skillful.' But because it is possible to develop what is skillful, I say to you, 'Develop what is skillful.' If this development of what is skillful were conducive to harm and pain, I would not say to you, 'Develop what is skillful.' But because this development of what is skillful is conducive to benefit and pleasure, I say to you, 'Develop what is skillful.'"

In MN64, the Buddha discusses the conundrum of identity and the presumed immaculate innocence of infants:

MN64:3.3: For a little baby doesn’t even have a concept of ‘identity’, so how could identity view possibly arise in them?
MN64:3.4: Yet the underlying tendency to identity view still lies within them.

And when that underlying tendency manifests:

MN64:5.2: Their heart is overcome and mired in identity view,
MN64:5.3: and they don’t truly understand the escape from identity view that has arisen.

Although we might search for the escape from identity ourselves, the Buddha also says:

AN2.126:1.1: “There are two conditions for the arising of right view.
AN2.126:1.2: What two?
AN2.126:1.3: The words of another and proper attention.

The Buddha himself had many teachers, including Buddha Kassapa in a previous life. And he listened with proper attention.

Listening with proper attention, we might come to understand something quite important...

If identity view arose, then it must also disappear, hopefully before our deaths in this very life. Impermanent phenomena are unsatisfactory. Impermanent phenomena cannot be a foundation for steady contentment and peaceful equanimity. So, rather than focus on identity, we turn away from identity. And any step away from identity view is a step towards the Noble Eightfold Path.

MN64:10-12.4: They contemplate the phenomena there as impermanent …
MN64:10-12.5: They turn their mind away from those things …
MN64:15.4: If they don’t attain the ending of defilements, they’re reborn spontaneously … and are not liable to return from that world.
MN64:15.5: This too is the path and the practice for giving up the five lower fetters.”

That is how we all start on the path. We start on the path by questioning the value of identify view and we listen to others with proper attention. And with insights gained, we deepen our practice, gradually becoming living proof of the Buddha's words.

Identity view is a false prophet. Look beyond.

MN62:3.2: “Rāhula, you should truly see any kind of form at all—past, future, or present; internal or external; coarse or fine; inferior or superior; far or near: all form—with right understanding: ‘This is not mine, I am not this, this is not my self.’”

So we really don't need to know about the why of identity view. We do need to examine our assumptions carefully and note that suffering inevitably follows when we listen to identity view. In a burning house, it's better to get out the exit than to wonder why there is an exit.