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I'm searching for a reference of an undecidability proof that is as simple as possible and starts "from scratch".

With "from scratch" I mean that it does not use some other undecidable problem to prove some undecidability (which is the usual case), I cannot wrap my mind about how proving undecidability that way (without a previous proof) could be possible.

This question may be inspiring: An example of an easy to understand undecidable problem

Also, I know this is probably not very objective, but it is important to me, it should be something as simple as possible, hopefully enough so that even I can understand it.

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Trylks
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to some degree all refs on the subject have a formidable inherent complexity due to the subject matter. however, here is a classic, highly accessible ref on Gödel's thm that may be helpful, written in "popular science" style by a philosopher & mathematics historian for a broad audience, breaking it down into intuitive everyday language.

here are some other similar but more technical refs that may be helpful

there are also many refs on Turing's halting problem. one worth mentioning, a step-by-step walkthrough/tour of the original proof, but which is very advanced due to retaining all the mathematical complexity/detail:

on the other hand most of the proof complexity of the halting problem is associated with the proof of the existence of the Universal TM, wikipedia has a pretty good outline. this can be understood as a simulation or emulation of one machine by another. therefore studying the theory of machine emulation (now quite frequently applied with video games) may be helpful.

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