Yes, David defeated Goliath
“David against Goliath” “Few Against Many” was one of the ethos on which the story of Israel was built upon. The idea that the young and small state of Israel succeeded against all odds to repel the invasion of the armies of Transjordan, Iraq, Egypt, Syria, Lebanon, Saudia… with the assistance of many other Arab countries.
This is also why he is one of the focal points of the attacks of the “New Historians”, the New Historians said that Israel had the advantage both in manpower and in arms, and denied what they regarded as the myth of a heroic liberation war of the few against the many and so, to try to conclude that the 1948 war was not a war for the survival of the Jewish people against aggressive Arab armies, And so it contributes in a sense to the Nakba narrative.
On the surface, it seems that the facts supporting this assertion, just looks at the manpower of both sides, it is clear that the Israeli side had a much greater manpower over its enemies.
So is this the truth? Was the State of Israel really more powerful than its enemies at the time of its establishment?
Manpower and actual Fighters
Here’s a small detail that most of those “new historians” do not give so much attention to:
As Yoav Gelber explained, This statistic, however, is somewhat misleading.
The Israeli figures included
the IDF’s entire logistic infrastructure, which lacked a parallel among the
invaders whose supply depots and base installations remained at home 
Asaf Agin explains that in the absence of preliminary sources, the researchers relied in their calculations on the “conscripts” of the IDF and these distorted the picture since the “services” component was not taken into account. For example, at the end of July 1948, only 42% of the conscripts were field troops and more than 25% were service (logistics, support, clerical, etc.). At the same time, the Arab’s data were the full fighters and hence a sharp distortion in the assessment of the balance of power 
Another breakdown of the forces shows that only some of the recruits were actual fighters 
On April 1, 1948. The Jewish Defensive Force had a total of 21,775 conscripts, of which 15,815 were field fighters.
On July 17' it was 63,586, of which 27,428 were field fighters.
When considering this data, the result looks like this:
On the day of the invasion of the Arab armies, on May 15, 1948, the Jews had a defensive force of 22,363 against an Arab attack force of at least 36,450
What the numbers do not include is “Faza”, The Faza’a militia was the system where an Arab sheikh could call up the males in his district for attack or defence, The potential numbers are estimated at 50,000, but most of their activities was limited to their village area
At its first session on May 16, the provisional Israeli government heard prime minister and minister of defense David Ben-Gurion offer a stark survey of the military situation. “The number of [Jewish] recruits has exceeded 30,000, but only 40% of them are armed due to the lack of rifles,” he told his colleagues. “The [Arabs] are using artillery, aircraft and tanks, while we have a single tank and a number of [captured] British armored cars.” Ben-Gurion was confident that Israel would be able to turn the tables on the invading armies after the arrival of newly bought weapons. Until that happened, he anticipated a period of great uncertainty. “In my opinion we’ll be able to teach them a lesson they’ll remember for generations,” he said. “But for the time being the situation is extremely serious.” 
Israel suffered from a lack of heavy equipment from the start of the war. According to Morris, the Israelis had 12 armored cars of which four had canon, three tanks, three half-tracks and three patrol vessels. By the end of May Israel had acquired 10 additional tanks and about a dozen half tracks. Morris credits Israeli forces with about “one hundred armored trucks and personnel carriers,” but most of these, he admits were homemade vehicles created by “armor” plating trucks.
The Arab armies, according to Morris, had about 75 combat aircraft, 40 tanks, 500 armored vehicles, 140 field guns and 220 anti-aircraft and anti-tank guns. 
Morris also tells us that by July the Israelis had about 300 armored cars and half-tracks, 15 tanks, 150 artillery pieces and over a dozen fighter aircraft including Spitfires and Messerschmitt 109s (or Avia — a Czech imitation), as well as 16 bombers and 50 light and transport planes. while the Egyptians had at least 132 light tanks and 3 Sherman tanks, and the Syrians had 45 Renault R-35 and R-39 light tanks. 
Examples from the field
A collection of anecdotes that shows what was the state of balance of power in the war:
The Jewish Quarter in Jerusalem
Machine guns: 2
Manpower: 700 +Hundreds of gang members
Machine guns: 25
Mortars: 6 (4 heavy)
The British estimated that in the battle for Haifa, some ‘2,000’ Arab militiamen were set against ‘400 trained Jews backed by an indeterminate number of reserves 
Battle of Mishmar HaEmek
On 4 April 1948, about 1,000 Arab Liberation Army (ALA) militiamen launched an attack on the kibbutz. They were initially opposed by 170 Jews and later, two companies of the Palmach, “less than 300 boys.”
Battles of the Kinarot Valley
On May 20,
Some 380 Jewish fighters stopped an attack of 1,500 Syrian soldiers armed with 12 tanks and 18 armored vehicles 
Contrary to the claims of the “Mythbusters”, the young state of Israel really had to survive an attack by Arab armies with a quantitative and qualitative advantage, in manpower and arms.
Against all odds.
 Yoav Gelber, Palestine 1948, 2006 pg 12
 הקרב האחרון להצלת מיתוס “דוד מול גוליית” במלחמת השחרור
 ההיסטוריה של ארץ-ישראל’, כרך עשירי: מלחמת העצמאות (1947–1949) By Yehoshua Ben-Arieh pg 128
 Herzog, Chaim and Gazit Shomo, The Arab Israeli Wars, Vintage Books, N.Y. 2005. pg 47–48
 Palestine betrayed by Karsh Efraim pg 236
 פלישת הצבאות הסדירים של מדינות ערב - 15/5/48
 Righteous Victims by Morris, Benny, Alfred Knopf, 1999. pg 217
 1948–49 War of Independence Arab TO&E
 הרובע היהודי במלחמת השחרור
 Birth of the Palestinian Refugee Problem Revisited by Benny Morris pg 192
 Chaim Herzog (1982). The Arab-Israeli wars: war and peace in the Middle East. Arms & Armour Press. p. 27
 Kimche, J. (1950). Seven fallen pillars pg 215
 Valley at war by Assaf Agin pg 241