First of all, the common idea that Israel was ever mostly (or even primarily) Holocaust survivors is flawed. Jewish immigration from Europe occurred at progressively higher levels during the 20th century before WW2. Many of those immigrants, especially during the 1930s, were German Jews fleeing the Nazis (although this is still before the Holocaust). The immigrants after the Holocaust were politically important, because they visibly agitated for a relaxation of British limits on immigration to Mandatory Palestine, but they were not the demographic core of Israel.

Many of the earlier waves of immigrants were from Eastern Europe, who would've spoken Yiddish natively. But closely linked to the whole Zionist project was the Hebrew Revival Movement, which encouraged the revival of Hebrew as a common language. This meant that Jews in Palestine actively attempted to teach new immigrants Hebrew, and encourage its use. It also meant the harsh rejection of Yiddish as "diasporic", so there were internal squabbles in the Jewish community about having Yiddish theater or Yiddish movies (both of which were actively protested).

The huge wave of immigrants from Germany in the 1930s would've spoken Yiddish. German Jews historically spoke Yiddish, but by the 20th century Western Yiddish was very nearly extinct, having been totally replaced with Standard German.

There were small numbers of immigrants from non-European countries before Israeli Independence, but soon after independence the situation for Jews in Middle Eastern countries became very percarious, and entire Jewish communities migrated to Israel in a few years. There also were various communities of Jews living there prior to any immigration, who mostly spoke Arabic. The huge Jewish communities in Yemen, Iraq, Syria, and Egypt almost completely relocated (most all of whom spoke Arabic, with a small Aramic-speaking minority). This wave of immigrants completely overwhelmed Israel's ability to absorb people, and a substantial population of people lived in migration camps. Later on there were waves of migrants from Algeria (though many moved to France instead) Iran, the former USSR, and a variety of other places.

In all these cases, Jews generally did not speak Hebrew fluently upon their arrival. Many had some ability for religious purposes (probably reading in many cases, but Hebrew has always been a common language for writing religious texts too), but that wasn't the case for everybody by a long shot. Israel developed a system for educating immigrants in Hebrew called the ulpan, where people would learn intensive Hebrew courses for several months. There were certain things built into the infrastructure to help immigrants, such as newspapers having "new immigrant" editions, which included vowel markings for unusual words and spelled out acronyms (which have always been a common feature of written Hebrew).

Realistically, no other language was going to work for Israel. Yiddish had the natural advantage of being the native language of a huge number of Jews in the early part of Israel's history (and is close to German, which was the language of the immigrants during the 1930s), but it was viewed as a "diasporic" language and thus harshly rejected by the Zionist movement in general. After a few years a large proportion of Jews in Palestine either were young and spoke Hebrew natively, or had been using it for daily life for many years, making its status secure. By the time the large immigrations from Arabic-speaking countries happened, Hebrew being the main language was very much a done deal.

Nowadays, Yiddish is a fairly small minority language, relegated to the elderly and some ultra-Orthodox communities, as in the US. Besides Palestinians, who speak Arabic, there are areas with more immigrants from particular areas where another language is easy to find (Russian being by far the largest, but also French, Spanish, and Amharic), but Hebrew is the near-universal native language of native-born Israeli Jews.