The question is how large it will be. Although it's highly unlikely the British and the UN would tolerate an Israel that controlled the West Bank, that's more likely than no Israel at all.
I don't think it is up to the British or UN. Any Jewish state is going to lead to war with the Arabs, and the actual borders all depends on what the ceasefire lines are when the war ends. So the question is what are the plausible ways the 1948 Israeli-Arab War could be different that it allows changes in the borders one way or the other?
If the Arab powers had mobilized their forces greater than they had, then it is very possible that they could have won the war completely leading to no Jewish state. However, it is probably not realistic to expect the Arab powers do that. That is an option that only exists in retrospective. The Arabs at the time just don't think it is necessary or prepared to pay the cost to do so during the war. So I think it is more realistic to assume that that the better POD assumes greater Israeli military success.
One possible area is that the Israelis take the town of Latrun very early on (say early May). That would lead to an early link up with Jerusalem. It would preserve Israeli strength squandered on failed attacks and allow them to attack elsewhere in the West Bank. It seems that the Israelis did not initially consider Latrun to be important until too late by which Jordan's Arab Legion took it. If they had realized the importance of the town early on, they could have taken it early. This allows the Israelis to build up for a West Bank offensive in the second phase of the war (after the first ceasefire in June-July 1948).
When the ceasefire ends in July, the Israelis are able to take the entirety of the Old City of Jerusalem and break out into West Bank. I assume the primary objectives of the Israelis would be to secure Bethlehem and Hebron (because of their historical importance) and drive to the Dead Sea in order to separate the West Bank into southern and northern halves. If successful, it puts the Israelis in good position to seize control of the entire southern half of the West Bank (Judea) later in the war. Then in July, the second cease fire happens. ITTL, the Israelis have much greater control of the West bank than OTL. They have the Old City, Bethlehem, Hebron, and have cut the West Bank in two at the Dead Sea.
Another important POD is that no Jewish extremist assassinates Count Bernadotte. When the Lehi organization assassinated Bernadotte on September 17, 1948, it hurt the image of the Israelis. When Ben-Gurion asked his cabinet to approve an attack on Latrun afterwards with the intention of conquering all of the West Bank, the cabinet voted no because it was concerned the international consequences would be too severe combined with Bernadotte's recent murder (as well as any other issues like concerns about how much of the Arab population would remain). Let's say with the earlier POD, the Stern Gang never assassinates Bernadotte so that the Israeli government does not fear losing international support. Instead, the greater Israeli success on the Jerusalem/West Bank front has helped the government consolidate control over the militant groups (like the Stern Gang). IOTL, the Stern Gang was integrated into the IDF on May 31, 1948 but the Jerusalem members remained independent (I assume because Israeli control of Jerusalem was tenuous because of the siege). ITTL, the holding of Latrun consolidates the government's control of Jerusalem and the Stern Gang there can't do whatever they like.
The second ceasefire ends in October and the Israelis overrun all of Judea. The success there allows for an offensive into the northern half of the West Bank (Samaria) and an earlier offensive into the Gaza strip (IOTL Operation Horev launched in late December was to cut off the Egyptians in Gaza, but British pressure at end of the war ended the offensive before it completed their objectives). I assume any offensive into Samaria would be designed to expand the zone around Jerusalem and to control the access across the River Jordan.
I highly doubt Israel could seize the entire mandate before international pressure creates an armistice, but it could definitely get a lot more of the West Bank with some lucky breaks. If Israel succeeds in cutting off all the West Bank from Jordan, then the result could ironically be an independent Arab state in the West Bank (as IOTL it was annexed directly by Jordan) in 1949. Although I assume failure of the Arab powers to recognize Israel will mean Israel won't recognize a Palestine. The rest of the world though will probably recognize both. However, I think it is theoretically possible for Israel to run the board and seize Gaza and the West Bank in 1948/1949.