The Cold War was a sustained state of political and military tension between powers in the Western Bloc (the United States with NATO and others) and powers in the Eastern Bloc (the Soviet Union and its allies in The Warsaw Pact). The POD in this scenario is that the Empire of Japan does not surrender after the atomic bombings of Hiroshima and Nagasaki. In fact, the United States and Britain will launch an invasion of Japan Homeland while the Soviet Union will invade Manchuria and Korea. By the way, sorry for my bad English, I'm used to speak French.
1945-1946 : Downfall
On November 1st 1945, led by Marshall Douglas MacArthur, 14 U.S. Divisions landed on Kyūshū from Okinawa on 35 landing beaches. Two days before, on orders of MacArthur, four nuclear bombs were dropped on Japanese stronghold. After 90 days of fights, 500 000 U.S. casualties were reported. Japan surrendered on May 2nd 1946, after 3.5 millions of U.S. casualties.
Meanwhile, the Soviet Union was not able to launch an amphibious attack on Hokkaidō. They rather decided to begin an offensive in Manchuria and Korea by August 1945. By the time of the invasion of Japan in March 1946, the People's Republic of China was a country - thanks to the help of Soviet Union - and Kim Il-Sung, a hero of the war against Japan, formed the People's Republic of Korea (Korea is not divided). Mao was killed by the NKVD and a more Pro-Soviet government is put in China, the Soviet Union gained some parts of Northern Manchuria and annexed Mongolia.
By the end of 1946, Indochina rebels against their French colonists. They are helped by the PRC and the USSR and it becomes the People's Republic of Indochina. By the following years, Communism has spread in Siam and Burma.
Following World War II, the Soviet Union becomes more powerful than in OTL, they have put a more friendly regime in China. The United States sends billions of money to reconstruct Japan and even begins to build an army called The Japanese Defense Forces (JDF) to prevent any aggression from Korea, China or the Soviet Union. In 1948, the Greek Civil War ends with the Communist revolution. Israel is found in May 1948.
The country changes his name to the Democratic Republic of Greece. With all Eastern Europe allied with the Soviet Union, Turkey decided to stay neutral in 1949 when the United States, Canada and Western European countries formed NATO. But Saudi Arabia, who was allied with the United States, feared the Soviet expansion in the Middle East and created the Baghdad Pact including USA, Canada, United Kingdom Saudi Arabia, Iran, Iraq, Syria, Israel, Yemen and other smaller countries in the Arabian peninsula to stop the Communism in the region.
1950-1958 : The fear of Soviet Invasion
During the 1950s, the Space Race and the Arm Race begins.
In the 1950s, many Europeans feared of a soviet invasion of Western Europe, especially in West Germany and Austria. But no military actions were made in the early 1950s. In 1955, Warsaw Pact is created.
The same year, Austria is neutralized and occupation of its territory seized. In 1956, Nasser nationalize the Suez Canal. Some times later, Hungarian Revolution of 1956 is crushed and many civilians are killed. Later that year, Israel, France and the United Kingdom invade Egypt in the goal of removing Nasser from power but Soviet threats of launching nuclear attacks on Britain, France and Israel made them removing their armies.
In 1957, Sputnik I and II are launched. In 1958, a failed coup happens in Iraq, the British government sends more troops to keep the country safe from socialist revolutions.
In November 1958, Soviet Premier Nikita Khrushchev issued an ultimatum giving the Western powers six months to agree to withdraw from Berlin and make it a free, demilitarized city. At the end of that period, Khrushchev declared, the Soviet Union would turn over to East Germany complete control of all lines of communication with West Berlin; the western powers then would have access to West Berlin only by permission of the East German government. The United States, United Kingdom, and France replied to this ultimatum by firmly asserting their determination to remain in West Berlin and to maintain their legal right of free access to that city.
1958 : The Battle of Berlin.
Following the six months of ultimatum and the certainty that the Caucasus was well defended (Turkey being neutral would not attack Azerbaijan), the Soviet forces began the all-out invasion of West-Berlin.
Meanwhile, Fidel Castro was taking power in Cuba.
On May 8th 1958 (13 years after World War II), Soviet and East German armies crossed West Berlin with air attacks on American and British positions. In a few days, the Americans began atomic bombing of East Berlin and Poland and they soon took the advantage. The Soviets retaliate by bombing Hanover, Hamburg and Bonn. On June 6th, with the loss of more than a million people (civilians and military), Soviet Union and NATO make peace and Germany is unified as the Democratic Republic of Germany (Warsaw Pact). On September 1st 1958, Germany is unified. Denmark who was also attacked rejoins the Warsaw Pact and Luxembourg is annexed by Germany.
Some historians consider the battle of Berlin of 1958 (Not to be confused with the battle of Berlin of 1945) as World War 3, even if it just lasted 1 month. The United States sends about 20% of its troops to France and England to make sure that they would not lose another war. Turkey joins NATO in exchange of billions of dollars in aid to improve their economy.
1959 : Invasion of Cuba
When the Americans saw that Fidel Castro took power in Cuba, they decided to invade the islands in fear of Communism in America. On New Year's Eve, The 1st Marine Division and the 82nd Airborne Division attacked La Havana while Rangers from Guantanamo attacked East Cuba. Within five days, they overthrown Fidel Castro, but the American image internationally dropped.