I’ve always considered the transition to have started in the beginning of the 20th century, when the Ben-Yehuda’s works became pretty prominent. If I recall correctly, the first seminary where Hebrew was a subject was opened in 1904. Yet, recently I found another point of view: Hebrew started spreading after the State of Israel was proclaimed, which initiated a tendency of this transition. Which point of view is more accurate? Is there any historiographical materials on that topic?
It's an even more complicated story than that! In fact, in the 19th C, there was a strong literary scene of modern novels in Hebrew among European Jews before there was a strong Yiddish literary scene. It still wasn't really spoken until Eliezer ben Yehuda's work in Ottoman Palestine, which was partially based on a marketplace Hebrew that was arising from the interactions of different Jewish communities which did not have any languages in common but liturgical Hebrew.
One example of Hebrew winning out well before the establishment of the state of Israel was when in 1914, the Technion (a university in Haifa) decided to switch the language of instruction from German (not Yiddish) to Hebrew.
You are correct that Hebrew started becoming the primary language of all Jews in the region after the establishment of the State of Israel in 1948, and not just for certain segments of society.
I can't think of that many in depth sources, but I remember that the Spring 2017 issue of the Jewish Review of Books (https://jewishreviewofbooks.com/issue/spring-2017/) ran a few articles on the topic. Leyen gezinterhayt! (Yiddish for "read [it] in good health")
Did Hebrew replace Yiddish?
I would say the decline of Yiddish and the rise of Hebrew are separate.
Yiddish declined suddenly because of the Holocaust. It arguably would have declined anyway, but it did decline in every country where the surviving Yiddish-speakers ended up - mainly the US and the Soviet Union, where they switched to English and Russian.
The rise of Hebrew happened in Israel. The majority of ancestors of Israelis are not Ashkenazim, but Sephardim or Mizrahim or other people whose ancestors mostly spoke some other language, most commonly some form of Arabic.
So Yiddish, i.e. Judeo-German, was mostly killed by the Holocaust, irreplaceably, and Hebrew mostly replaced Judeo-Arabic, although many remain bilingual, so it's not necessarily replacement.
Right now, Yiddish speaker numbers correlate with the numbers of certain Orthodox communities, which are growing. I would need to see evidence that they somehow anti-correlate with Hebrew speaker numbers.
The languages which saw a high proportion of their speakers switch to Hebrew are smaller Jewish languages like Ladino, Judeo-Georgian, Judeo-Tat and Jewish Neo-Aramaic. But even in those cases, it's possible more were lost to the usual suspects like Russian, Persian and English.
Modern Israeli Hebrew is replacing the other Hebrew pronunciations preserved in diaspora, even though they are more historically correct. But the modern Israeli Hebrew pronunciation is influenced by Yiddish pronunciation, so that's Yiddish replacing Hebrew, not Hebrew replacing Yiddish.
The answers above are excellent and on track.
What is not clearly discussed is that the rise of Hebrew, pre-1948 (e.g. in the decades prior to the establishment of the State of Israel) was actively promoted by the Zionist movement. This is the cause of the literary scene discussed, and the decision of the Technion to switch to Hebrew.
In the early 1990's I spend a lot of time with an elderly man who knew Yiddish well, had been born in Latvia, and had spent most of his life in the U.S. He had been very active in various Zionist causes for his whole life. He spoke to me of the many sins he had committed against Yiddish (in a Yiddish speaking Jewish community in the U.S.) in the course of promoting Hebrew.
Yiddish was killed by the Holocaust. (Not only villages and people were murdered.) However, as the language of "old oppressive-to-the-Jewish-people Europe," the new, young movement of Jewish renewal had its knives out for Yiddish in the decades before and after the Holocaust.