Maybe what the questioner means is: how do we reconcile the age accepted in Judaism, which counts 5778 years since the creation of the world, with the scientific determination of an estimated age of about 13.8 billion years?
True, the view is well known that claims that the six days of creation were not 6 units of 24 hours, since that refers to the earth’s rotational cycle around the sun, whereas according to the Torah the luminaries were only set in place on the fourth day.
The question is: what is the meaning of the number accepted in Judaism (5778)?

If so, the questioner answered himself at the beginning of the question: interpret the sacred texts in more and more creative ways.

Okay. The question is what that creative interpretation is that could explain the Jewish age of the world.

It can be understood as a metaphorical description of the stages of the world’s development. Each stage is a biblical day. And especially since all this comes to teach us norms, not facts (a moral hierarchy among the inanimate, plants, animals, and human beings). The number of six thousand years describes familiar human history since “the first man” (who is not what would be defined as the first Homo sapiens, about whose appearance there are also huge disputes among researchers).

If so, who is that “first man” in your opinion? And why is it important to count time from his period?

What do you mean, who is he? What was his name? Adam.
The counting really isn’t important. They had to establish an origin point for the calendar, and they used for that purpose the beginning of the biblical narrative.

What I mean to ask is, if the first man is not the first Homo sapiens, then who is he? What sets him apart? After all, around six thousand years ago there were very many human beings completely similar to him, and besides, the Torah says that he indeed was the only human in the world.
And according to the claims of the scientific establishment today, six thousand years ago there were very many Homo sapiens wandering around the world, and no significant turning point happened, nor did any significant person live to whom the beginning of the count could be attributed. So again, what is the meaning of the number 5778 in the Jewish count?

The first human who moved from utilitarian survival thinking to abstract moral thinking.

The Mishnah speaks about the “lords of the field”—the letters n and m interchange there, and the intention is “people of the field.” The commentators explain them as wild men—hunter-gatherers who were still roaming around without culture. After them come the agricultural people. The agricultural people are already more civilized, but to a large extent remained demons, as Maimonides describes them in Guide for the Perplexed, Part I, chapter 17. That is, beings with a human appearance and civilized behavior, but without abstract moral rules. When the Talmud claims that the gentiles are suspected regarding bestiality, murder, theft, and more, it is essentially describing the gentiles as a kind of demons. On the one hand civilized, on the other hand lacking all moral restraints. The third group are those who have thought and morality—the first man and his heirs, Israel.

Maybe the first monotheist.

Now, a few advantages gained by adopting the evolutionary view:
Cain says: “Whoever finds me will kill me.” Rashi attributes this to the wild animals, but in light of the evolutionary view everything becomes simple. “Whoever finds me will kill me” refers to Homo sapiens who still had not received abstract thinking, but among whom the socially useful prohibition against murder still existed. They would hear about Abel’s murder at Cain’s hands and kill Cain without understanding that he had repented.
Cain builds a city for his son Enoch. True, in tractate Eruvin it emerges that a city can consist of a small number of houses, but clearly you don’t build a city for two and a half people. Cain builds a city in which Homo sapiens will live.
The midrash says that during all those 130 years when Adam separated from his wife Eve, he fathered demons—that is, Homo sapiens lacking abstract reason—from other female Homo sapiens.
Esau wants to kill Jacob. Esau knows the story of Cain and Abel and knows that an abstract prohibition exists, but Esau goes back to being a demon—that is, a utilitarian Homo sapiens acting like a mafioso.

I have no idea what sets him apart. The difference between me and various neo-Darwinians (what you for some reason called “the scientific establishment”) is that even though they also have no idea, they make emphatic claims. I don’t know whether at that time some special creature was not created with a different IQ or other traits (such as those described by Y.D. or Gideon), and that it was called the first man. As I understand it, there is no way at all to know this from research, and certainly no way to know that it didn’t happen. To know that it did happen—maybe that would be possible, if they found evidence showing that such a being came into existence then. But I haven’t seen such absence of proof count as proof.

There was not necessarily anything unique about the first man. The first man is the first in the genealogical lists of Israel and the ancient Near East (among all of them they count ten generations before the flood, and one of the names is Adam). He is the first one remembered, and all those before him were as though they had never been and were forgotten from the heart; with the first man, history effectively began. Why is he remembered? Apparently there was something special in his days. We can guess what it was: the invention of writing. That invention accelerated human development and also left documentation that, without writing, would have been forgotten. The genealogical lists too were transmitted in writing: “This is the book of the generations of Adam.” Book = documentation, not oral storytelling, as is well known (“and he shall write her a bill of divorce”). Note that the transition from prehistory to history also begins less than 6000 years ago in research. According to this, the ‘first man’ is not the first relative to the past described in the Torah’s ‘narrative time’ (q.v.), but relative to the present of those who received the Torah. He is the first from their perspective (obviously traditions about this man predated the giving of the Torah). It is not impossible that he did not exist at all. Maimonides and Ibn Ezra hint at this by the fact that 20 times in the story he is called with the definite article, “and the man knew…,” which proves that this is talking about the human species in general and not one individual. See in Gedaliah Nadel’s book in several places. If you want, send me an email and I’ll send you a comprehensive article about all this: giladstn@gmail.com