#1 problem is incompetent leadership of the Arab armies, inept Arab intel services, and poor training of Arab troops, which made an invasion a really bad idea.
Israel tries to nuke Damascus, Amman, and the Aswan dam with mixed results. The Arab countries are even angrier and swear that they will refuse to stop until every single Jew is out of Israel.
Jews still in Arab countries will be suspected of enemy sympathies and expelled, but probably not killed unless Israel successfully nukes a civilian center, in which case revenge killings will be common, claiming the lives of thousands minimum. Jews in Israel will be ethnically cleansed--somewhere between Mugabe's actions in Zimbabwe and Iron Guard Romania. No organized genocide, the Arabs don't have the infrastructure to do that and they're running on "these people invaded our brothers, kicked our brothers off of their land, then murdered our families", not obscure conspiracy theory crap, so they'll just open fire on civilians as payback for any nuked cities. This will destroy military cohesion but I'm assuming that the IDF has basically folded at this point (necessary for Israel to break out the nukes and gas). Most likely once actual mass killings start to happen, the international community (USA and USSR, basically) step in, USA setting up a perimeter as a safe zone for Israelis and the Soviets demanding that the Arabs stop immediately or the USSR will pull support because Leonid Brezhnev was too busy giving himself medals to enjoy nuclear war.
Israel will still exist, in a very limited and perpetually angry fashion. Tensions will be high and the USA will be tied down with actual military bases there. The Arab world will be vehemently anti-USA from early on, and likely pro-China once China drags its way out of the disaster that was Mao.
Sadly, the Lake Hula fish species that Israel drove to extinction so they could have some shitty farmland are still extinct. Hundreds of thousands of civilians will be dead, the bad blood will be insurmountable for centuries, and millions will be displaced. Complete disaster. Continued guerilla activity and border skirmishes for decades, political disaster and rigid factionalization over the issue in the USA, heightened Cold War tensions, small but significant chance of nuclear war with potential casualties in the billions.
The core thing with Israel is that the best way to avoid the whole situation we have today is for the Arabs to win in '48, likely due to a slower international intervention (from what I've read, the tide was turning when the UN stepped in). In which case, Israeli colonists are ethnically cleansed but Palestinian civilians are not, Jews in Egypt, Jordan, etc. are harassed for a few years/a decade or two by the Arab countries as potential enemy sympathizers, but without the existence of a Jewish settler colony making a point of being by, for, and about Jews while kicking Palestinians off their ancestral land and occupying bits of other Arab countries, these tensions likely gradually disappear under international pressure over the next half-century.