The USSR's pro-Zionist position was created in the late 1940's in part as a way of driving the British out of the Middle East. Soviet propaganda even called for Israeli and Arab armies to join together to defeat "British imperialism." And while the USA recognized Israel first, it was only de facto The USSR gave actual de jure recognition. And yes, the Russians gave the Czech Communists the go-ahead to supply Israel during the arms embargo (though it must be noted that the Zionists had begun negotiations with non-Communist Czechoslovakia, though that country fell to Communism in 2/'48, three months before the War of Independence.
However, for whatever reason, the Soviets turned against Israel after just a few years, this time ordering their Czech underlings to supply the Arabs. Soviet propaganda became anti-Israel and pro-Arab in the early '50's, even though the Israelis themselves at this time took a position of neutrality and refused to take sides in the Cold War. Israeli leaders at the time stated that they were unaware of any anti-Soviet Bloc activity on their part and could not understand Russia's hostility. But Russia had definitely become hostile and took the side of leftist Arabs like Nasser, though apart from a few days in the '50's they didn't break diplomatic relations with Israel until 1967 (and Cuba didn't until 1973).
The Six Day War is often considered the watershed event that caused the Communist bloc to become anti-Israel, but it had already long done that, despite helping Israel to come into existence.
Stalin came to suspect that Soviet Jews were Zionist spies. Before he died he was planning to have all Soviet Jews deported to Siberia.