With a POD after the declaration of independence of the state of Israel, how big can the state become? This does not include occupied territories like OTL West Bank, only land that has been directly integrated into Israel.
Eventually the Arab states would be forced to recognize Israel, and arrangements would have to be made for Palestinians. Israel would be a highly urbanized nation of possibly even 30-40 million by now with projections of nine figures within a couple of generations.
The problem with a 30-40 million population is that there isn't nearly enough water to go around, even with desalination.
Israel is not going to annex land that would threaten its Jewish majority, so to pull this off, you'd need to increase Israel's Jewish population.
As @Meshakhad said, an expanded Israel, in whatever form it takes, will need a fuckton of immigrants to allow for a permanent Jewish majority, at least at first (I also like OTL Joe Lieberman being PM.) However, to piggyback off that point, in order to make it workable long term, whether as an America-friendly state, a Soviet satellite, or the divided example I provided, a baby boom is a necessity. If Israel after 1948 draws in immigrants who have big families for at least a generation, whether by American osmosis, Soviet demand, or both, the population will be big enough to hold a significant amount of territory.
You all seem to be forgetting the other option which Israel has used historically, which is to simply reduce the Arab population of annexed lands.
Clearly the endgame is from the Nile to the Eurphrates
Due to butterflies, Truman narrowly loses the 1948 election to Dewey. Dewey begins a gradual shift of American politics towards a pro-Arab stance
Like 4.5 million Arabs in Gaza and the West Bank, million arabs in Israel proper, and million Arabs in Sinai?
It's one thing for the Israeli government to not let people who fled and their descendants return. It's another to actively drive people out.
Realistically the limits are the River Jordan and the West coast of the Sinai peninsular. Maybe Lebanon too.