How do I get started building a Rubik’s Cube solver from scratch?

Make sure to define your test cases from the get-go. Work towards passing those tests. It’s okay if your initial code isn’t pretty—focus on making it functional first. After getting it to work, you can refine and improve its appearance while ensuring that the tests remain successful.

For representing the state, I suggest using a face-based model (6 faces with 9 stickers each) instead of tracking each cubelet. It simplifies the rotation calculations significantly. Regarding algorithms, Kociemba's two-phase algorithm is a solid choice for C/C++ because it's much faster than BFS. But, if you really want to grasp the concepts, start with a straightforward layer-by-layer solver like CFOP. Python is great for quick prototyping, but C++ will give you better performance for repeated solves. The challenging part isn't really the algorithm; it’s making sure your move mechanics are free of bugs.

The way you represent the cube hinges on the algorithm you use. For instance, you could store a 3D array of colors (6x3x3), which makes sense but can be slow when manipulating extra data. Alternatively, you could represent the cube with 6 64-bit integers, using each byte for a face's bit-board; this method allows rapid bitwise operations. Another technique involves two arrays for corner and edge orientations, which is beneficial for pattern databases. Overall, if this project is for learning, I'd lean towards the 3D array method as it's the most intuitive.

I recommend starting by abstracting a lot of the complexity. You could represent the cube as a 3D array, maybe 3x3x6. The first step should be to create a Cube class with a print method to visualize the cube's state easily. You’ll also need a method for turns that takes in the side and direction of the turn. Don't forget to write some unit tests to validate that everything works as intended. This foundational setup will make it easier to build your solver on top of. Once you have that, try implementing some standard solving techniques and then experiment with more advanced methods like machine learning.