The USSR, under Stalin, was the FIRST (not second) country to recognize Israel from a legal standpoint (the USA did de facto, Stalin one-upped by going de jure) and this was only three days after Israel declared independence. It was thought that Israel would be pro-communist, pro-soviet. A lot of Jews in the Zionist movement were Russian, Marx was Jewish (His mother's father was a rabbi), Lenin and Trotsky were Jewish, a lot of the early communists were Jewish. I can see Stalin's strange logic in thinking he had a leg up.
The Jewish Autonomous Oblast had already been created in Manchuria/Siberia in 1934 and had reached its peak Jewish population of 30,000 in 1948... the very year of Israeli independence. It's possible that those people are allowed to emigrate to Israel if Israel was more pro-Soviet. India's pro-Soviet tendencies, based more on Pakistan's pro-American policies than anything else, may cause Israel and India to have even better relations creating a three-way make-shift alliance that could hamper Nixon's opening of China as a wedge against the Soviets. In OTL despite being Muslim both Turkey and Pakistan have historically had better relations with Israel than the Arab Muslim world and Iran, and this is in part because of their close USA relations. It is possible that Soviet influence causes a reversal- Turkey and Pakistan are more pro-Arab anti-Israeli, but Iran strangely enough ends up being a bit more tolerant. Wouldn't that be an interesting butterfly? Imagine Iran and Israel both have common Iraq enemy... Iran and India both common Pakistan enemy... Soviets and India both have China as a rival... You now have a loose bloc of USA, China, Pakistan, Turkey, Iraq, and the Arab World in general in a Cold War rivalry against Soviet Union, Israel, Iran, and India. Nasser meets with Ben Gurion and Kruschev after the Six Day War in a quaint country setting in the Crimea and shake hands and peace between Israel and Egypt. 1958 OTL United Arab Republic... does it still happen? If so Nasser and the Soviet Union forces Syria into peace with Israel. Jordan ends up being MORE anti-Israel given its ties to the US and Britain.