I would say that what humans do to learn has some elements of some machine learning approaches (Naive Bayes classifier comes to mind) on an unconscious level, but humans have a wild mix of different approaches to learning and even a single human employs many ways of capturing knowledge, and also, the imperfect and messy ways that humans capture and store knowledge is a critical feature of humanness.

I think we have to at least add the capacity to create links that were not learned through reasoning.

The difference in people is that our brains are continuously learning and LLMs are a static state model after being trained. To take your example about brute forcing more data, we've been doing that the second we were born. Every moment of every second we've had sound, light, taste, noises, feelings, etc, bombarding us nonstop. And our brains have astonishing storage capacity. AND our neurons function as both memory and processor (a holy grail in computing).

Sure, we have a ton of advantages on the hardware/wetware side of things. Okay, and technically the data-side also, but the idea of us learning from fewer examples isn't exactly right. Even a 5 year old child has "trained" far longer than probably all other major LLMs being used right now combined.

Contemporary LLMs are static. LLMs are not static by definition.

This is actually why I find a lot of arguments about AI's limitations as stochastic parrots very shortsighted. Language, picture or video models are indeed good at memorizing some reasonable features from their respective domains and building a simplistic (but often inaccurate) world model where some features of the world are generalized. They don't reason per se but have really good ways to look up how typical reasoning would look like.

To get actual reasoning, you need to do what all AI labs are currently working on and add a neuro-symbolic spin to model outputs. In these approaches, a model generates ideas for what to do next, and the solution space is searched with more traditional methods. This introduces a dynamic element that's more akin to human problem-solving, where the system can adapt and learn within the context of a specific task, even if it doesn't permanently update the knowledge base of the idea-generating model.

A notable example is AlphaGeometry, a system that solves complex geometry problems without human demonstrations and insufficient training data that is based on an LLM and structured search. Similar approaches are also used for coding or for a recent strong improvement in reasoning to solve example from the ARC challenge..