I totally agree! If anybody knows of something similar for artificial general intelligence I'm all ears, currently in the process of reading up on it.
Beginning your study of cognitive/computer science with GAI could be frustrating and fruitless, just as would be beginning your study of physics with superstring theory.
There are probably well-written and interesting GAI books/articles for laypeople, though, analogous to Brian Greene's excellent books on string theory.
You say "mathematics, cognitive science, and computer science at increasing levels of sophistication.". That's probably true, I'd recon a fair bit of biology, chemistry and physics is most likely also needed.
My question, though, is what specific branches of said subjects?