Why does the Rabbi assume not? What is the problem with it? And what does this have to do with the giving of the Torah?

If the Rabbi could elaborate a bit more, I would really be very grateful

I didn’t understand what there is to elaborate on here. I explained well what I had to say.
Jewish law did not exist before the giving of the Torah, and therefore the methods of acquisition were not necessarily like they are today. Even if once it was possible to acquire something, that does not mean that halakhically today it is possible to do so.
I assume not because there is nothing here to acquire. What do you want to acquire? The inheritance rights of the firstborn portion? That is something not yet in existence. Temple service? That no longer exists.

Is a firstborn inheritance really considered something not yet in existence? Seemingly this is like a palm tree for its fruits. And as for saying that this was before the giving of the Torah, the Rashash has already explained that monetary acquisitions are rooted in human reason and understanding, and according to that there should be no distinction between before and after the giving of the Torah. Though perhaps one could distinguish between ordinary matters and things whose source is in Jewish law, such as a firstborn inheritance and Temple service. Just as we find that a verbal declaration to the Most High is like delivery to an ordinary person. So too, even when it is not being given to the Most High, perhaps with an acquisition of something whose source comes from Above — that is, from halakhic law — there is a difference regarding acquisition.

What are you talking about? One does not sell the firstborn son but the birthright. This is not a palm tree for its fruits but the fruits of a palm tree.
And the Rashash’s view was before me when I wrote this. About that I will only say that his words are not universally accepted, so there is another aspect here to discuss. Also, even according to the Rashash, it is not correct that there is no difference between before and after the giving of the Torah. He only says that the laws of acquisition contain components that are meta-halakhic — they do not emerge from the Torah but precede it, not chronologically but essentially. But that does not mean that Jewish law will not change the laws of acquisition. When the Sages instituted pulling as the mode of acquisition for movable property, they changed the law that had previously been practiced and that existed before the giving of the Torah. The same is true of “the presence of all three,” and more.
In general, regarding something not yet in existence, the medieval authorities (Rishonim) and later authorities (Acharonim) already disagreed over whether symbolic commercial acquisition based on merchant practice applies to it. According to that, it is possible that before the giving of the Torah they could acquire something not yet in existence, but after the giving of the Torah this was voided.
And regarding your comment about a verbal declaration to the Most High, in my humble opinion it is unrelated to our issue. There it is acquired without an act because everywhere is in the treasury of the Merciful One. But that is not the case when the item is not being conveyed to the Temple treasury.

A. The birthright is the palm tree, and the inheritance is the fruits. So this is someone selling a palm tree for its fruits.
B. The Rabbi wrote that some disagree with the Rashash and that there is another aspect here to discuss. I would be very glad to hear more. I assume this is not the place for it. May the Rabbi find the proper place and write about it. (: (:
C. As for what the Rabbi wrote, that even according to the Rashash Jewish law can change the laws of acquisition — still, here we do not find that it did. Ability does not prove actual implementation. And where we do find it, how could they do that? הרי the item is not owned by him, so it turns out there is theft in his hand! Is it because a religious court may declare property ownerless?
D. If I understood correctly regarding a verbal declaration to the Most High — that it works by mere speech because every place is His domain, may He be blessed — what is the logic of that? Is it because then there is full intent even without an act? And if so, one should be able to transfer ownership by speech alone in the buyer’s courtyard without any act.
E. Thank you very much for the response, and have a good week

A. Birthright is a status, not an object. You cannot sell a status.
C. If Jewish law today does not allow a sale of something not yet in existence, whereas then it was possible, then there you have it — it changed.
D. That is a different question. My point here is that the analogy you made to the law of a verbal declaration to the Most High is incorrect. The difference is not in full intent but in the act of acquisition. If the item is in the domain of the Most High, then He acquires it through speech because this is akin to acquisition by courtyard. It has nothing to do with transferring ownership without an act or transferring an abstract thing in another context.

A. I know many palm trees that are a status. What is the halakhic equivalent of the concept of status?
D. I agree regarding the analogy. My question is: if I entered my friend’s courtyard with my yarmulke on my head, without any intention of effecting acquisition by courtyard, and then I studied Jewish faith and my intellect compelled me to become a heretic — in that case, could I sell my friend the unnecessary piece of cloth on my head, not by an act of acquisition but by speech alone, because the item is in my friend’s domain and is therefore akin to acquisition by courtyard? (I am assuming that acquisition by courtyard means bringing something into his domain with the intention of transferring ownership, which did not happen.)

When you use words of transfer, there is intention to transfer ownership. And if the item is in the buyer’s courtyard, then he has acquired it. I do not understand what is unclear here. But it seems to me that we have completely exhausted this. That’s it.

Why is this considered something not yet in existence? After all, the firstborn already has obligations and rights right now (for example, honoring his father, or the honor shown toward him). If so, he is now selling the entire package of those obligations and rights?

And in fact Ibn Ezra there writes that there are already rights at present. See there.

Rights and obligations are not sold. Even a debt, in principle, is not sold, except by rabbinic enactment (the presence of all three).