That's a great question! The short answer is yes, but it was rough going.
Let's first start off with a brief discussion of what was going on BEFORE the creation of the State. Israel was then British Mandate Palestine, and at that stage it was in something of a war of attrition with Jewish underground movements which were furious with it for both the way that it felt that it favored Arab residents of Palestine and the fact that the British were drastically limiting Jewish immigration of the survivors of the Holocaust, about 200k of whom were languishing in bad conditions in displaced persons camps in Germany. Many people made it in through the illegal Aliyot (ascensions)- most famously Aliyah Bet, in which ships (including the Exodus, later fictionalized in Leon Uris's novel) brought tens of thousands of survivors to Palestine, though about half were intercepted and sent to internment camps in Cyprus, Mauritius, and Atlit, Palestine. (My grandfather came through Aliyah Dalet, which instead of chartering special ships instead gave people the documents of legal residents of Palestine who they resembled physically so that they could sneak in.) Therefore, a major part of the stated motivation of those fighting for Israeli independence was free settlement for Holocaust survivors, among other Jews who might wish to "make aliyah" (the term often used to describe a Jew moving from the Diaspora to Israel).
The three years immediately following the declaration of the State in May 1948 brought more than 500,000 olim chadashim (new immigrants) from Europe (about half), Asia (35%), Africa (15%), and a smattering from the Americas. This was about as many people as had made aliyah in the 30 years between 1917, when the Balfour Declaration encouraged Jewish settlement in Palestine (then in the transition point between Ottoman and British control), and 1947. From 1948-51, Jews emigrated to Israel at a rate of more than 500 per day. This was very much in keeping with the desire of the founders of the State to make it open to Jewish immigration, whether from the outset in the new State's Declaration of Independence or in 1950 with the institution of the Law of Return, which opens immigration to all Diaspora Jews who wish to come. Jews were coming in the early stages from DP camps in Germany, from Bulgaria (which was allowing Jewish emigration for the first time since the 1920s), from Poland and Romania (which sometimes opened and sometimes closed opportunities for emigration, requiring Jews to snatch those opportunities when they could), and from the internment camps in Cyprus and Mauritius where the British had placed all of the Aliyah Bet immigrants whom they had caught. They also came from North Africa, Yemen (where the rescue mission was called "Operation Magic Carpet"), and Iraq, where the founding of Israel had made the Jewish residents of many of these countries hated and where Jews were being all but expelled, facing incredible hostility from the government and general population which often erupted into violence, propelling Jews to leave with whatever of their possessions they could carry. In Iraq in particular, in 1950 the Jews were given a one-year window in which to leave in return for relinquishing their Iraqi citizenship- while the Iraqi government only expected 10,000 Jews to leave, in fact 120,000 left in what was later called Operation Ezra and Nechemia (after two leaders of the return of the Jews from the Babylonian Exile in the late Biblical period).
The thing was, for all that the new Israeli government felt that accepting these people was in some ways its raison d'etre, the country simply didn't have the capacity to accept all of them. There were already some immigrant camps, but they were already filled, and were themselves suffering from a lack of space and resources. Some immigrants were put up in abandoned Arab villages. David Ben Gurion, the first prime minister of Israel, noted the fact that immigration was tremendously exceeding the State's ability to absorb them, but that this was "fate's verdict" and immigration could not be stopped for that reason. Bear in mind, as well, that while most countries at that time (which still by and large had the extremely restrictive immigration policies of the interwar era) would only accept desirable immigrants who would bring money, skills and health with them to their new homes, Israel took EVERYONE, no matter how poor (or newly poor, thanks to the hardships in place due to the conditions in their countries of origin), sick, old, or unable to work. Since Israel could not afford the absorption of these immigrants, it used money from organizations like the Jewish Agency, the American Jewish Joint Distribution Committee (or the Joint), and others to fund the settlement of the immigrants using money raised from Jewish communities abroad (mostly in the US). It also used some money from the German and US governments (often in the form of loans).
With the realization that the immigrant camps were not viable solutions (they had hundreds of people living in dormitories and unable to work), the Jewish Agency decided to create ma'abarot, or transit camps, which could be more family-friendly and could be the immediate precursor to moving into permanent housing, but these camps were often just as flimsy, dirty and ramshackle as the immigrant camps, with no electricity and little running water. While in the immigration camps the residents had received food and medical care at the government's expense, in the ma'abarot they worked at menial jobs in order to support themselves and their families. While few immigrants were spared the poor conditions of the temporary housing in which they were placed, the ones most likely to be placed in poorer areas in the periphery were the Sefardic Jews from Africa and the Middle East, called the Mizrachim by the (mostly Ashkenazic) pre-State residents. While many of the residents had been wealthy professionals with opulent homes back in Iraq or Egypt, in Israel they lived in horrible conditions and had little employment open to them but manual labor.
Those who were already living in Palestine at the time of its becoming Israel were generally overwhelmed and not thrilled with the massive wave of immigration. They were coming off a massive war of independence and wanted to peacefully build their state, and were not eager to participate in the absorption of hundreds of thousands of new immigrants. Even those who were employed by the government and the Jewish Agency and Joint were often disgruntled at the huge numbers of immigrants, and, unlike their colleagues who were directly assisting in the immigration, felt that immigration should be done in correlation with capacity for absorption. Most ma'abarot were built, while relatively close to the center of the country, generally far from the big cities in the center of Israel (with the exception of Jerusalem), and so the average urban Israeli never saw one and never encountered a new immigrant who lived in one. Most of them were immigrants themselves, and were frustrated to read in the papers about the difficulties that these immigrants had with being absorbed, when they themselves had managed fine through adversity! (While this is from 20 years later, this skit* from Israeli comedians Arik Einstein and Uri Zohar basically retells the history of the waves of aliyah in terms of immigrants looking down on the immigrants who came immediately after them.) The new immigrants were often treated with derision, both the Mizrachim (for generally somewhat racist reasons, as they were seen as backward and un-Western) and the Holocaust survivors (for reasons which I discuss here). The Mizrachim, and specifically the Moroccan immigrants, were seen as thugs and criminals. Israelis who had been building a national identity based on Hebrew language culture and Zionist ideals were afraid that they would be diluted by massive numbers of Jews of many cultures and languages who might not share these ideals. The kibbutz movement, one of the proudest symbols of Israeli culture and self-determination, refused to employ new immigrants as they felt it a violation of their socialist ideals to bring on outside labor, though they had taken in a number of Holocaust refugees before the establishment of the State.
*Warning- I just rewatched this, and the subtitles aren't nearly as good as I remembered- you might not enjoy this if you don't speak Hebrew
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