Can one learn first Turing machines, then to build core of OS, then hex editor, then C compiler, the some theorem proving software like Coq and then prove that the OS is free from bugs etc.
Can you learn anything in any arbitrary order if you put in enough effort? Sure. But there are things you're glossing over.
You never really mentioned what your learning goal is, but I'm going to assume your goal is to learn skills that you could build a career out of, rather than just having a look around the history of CS as a recreational exercise.
If it is a recreational exercise, then you can just do what you want. It's the equivalent of freely walking around in a museum and looking at whatever you're interested in.
0. Computer science vs computer science
The answer depends on what you mean by "computer science". If you're purely focus on the algorithmic theory of it all, then this follow the same general approach as math and therefore you can/should learn it the same way.
But the examples you use in your question seems to be much more focused on practical applications of CS, rather than the theoretical algorithmic. Here, the same logic does not hold true, and the rest of the answer is written to address "software development" rather than theoretical computer science.
1. Obsolete means useless
For example, if you want to learn how to build a car, you could start by learning to build a cart, and you could take a deep look at the intricacies of minimizing wear and tear on a wooden axle. But it'd be a lot of effort to learn something that is no longer relevant today, and it won't meaningfully contribute to your experience as a car mechanic.
Similarly, if you want to be a C# developer, there's no point in learning Assembler first. Just because Assembler came before C# and somewhat inspired the C# creators does not mean it's beneficial to learn it now that C# is a well established platform on its own.
2. Catching up to current technology
Don't forget how fast the industry moves. If you spend time and effort learning the old and outdated things, by the time you're done learning about them, some things that were current back when you started may be outdated by now, so you'd have to learn them too.
The software development field moves at a breakneck speed and it's already hard for professionals who are already at the forefront to keep up with new developments. As a learner, you will be slower (due to inexperience) and you have more ground to cover (because you're not at the forefront).
Sure, if you focus on a particular specialization of software development, you're going to have less ground to cover, but I'd advise against starting out with tunnel vision. Programmers are incredibly sensitive to the "when you have a hammer, everything looks like a nail" adage and if you teach yourself a limited skillset, you're likely to end up trying to use this skillset in inefficient ways because you don't know of a better way.
3. Conventionalism over universalism
Math is different. Math is universal, and the core principles have not changed for millennia. You can't really learn the newer things without understanding what they are based on.
Good mathematics are a matter of universal correctness. You can independently rediscover math and end up with the exact same end result.
Programming paradigms, however, are fashionable. It's not about what's universally correct, but rather about what works. In a different ecosystem, different paradigms prevail.
Good programming is a matter of convention. If you rebuild programming paradigms from the ground up, you are likely to end up with completely different paradigms. Even if they are as correct, they will still be fundamentally different from the current paradigms and you won't be a compatible employee for most (if not all) companies.
Way back when processing power was the biggest bottleneck, low-level programming reigned supreme as it gave developers control over every minor aspect of the application in order to squeeze every bit of performance out of it.
Nowadays, with processors being everyday powerhouses, the bottleneck has shifted towards maintainability of the codebase. The prime focus now is human-readable and change-friendly code.
The rift between the old and new lines of thinking are massive. They share little to no common ground anymore, and this means that learning one way is mostly going to teach you things that the other way labels as "bad practice". If you err on the side of learning the old way first, you're going to have to make every (nowadays) bad practice mistake.
4. Divide and conquer
Essentially, every mathematician needs to understand math from the ground up, from the axioms to the specialized applications thereof. You can't be a mathematician if you don't understand 1 + 1 = 2.
But software development specifically aims towards ensapsulation of responsibilities. I don't know how a compiler works internally, but it doesn't matter because someone already made it. I don't need to know how it works for me to do my job, I just need to use it.
What you're suggesting is akin to saying that you need to understand chemical combustion, oil refining, the vulcanization of rubber, ... and car manufacturing before you can properly drive a car, and that's simply not the case. Knowing how something is built and knowing how to use it are two different things, often important to different people.
Therefore, you don't need to know how things like the C compiler or your OS have been built in order for you to use them (for software development), and it's much better to not look under the hood until you are experienced enough to look under the hood and actually understand what's happening.
5. Historic knowledge is a nice-to-have
Don't get me wrong, I still like looking at older technologies once in a while, but I do not rely on that for understanding modern technologies. It's always interesting to know more about the evolution of a field and how things have changed.
But if you're focusing on current-day-employability (which is what I assume your learning goal is), then obsolete technologies are not relevant for acquiring the needed skills.
