The Cold war didn't have a definitive start date. Traditionally, it is pegged in March 1947 with the Issuance of the Truman Doctrine. The Truman Doctrine was, "to help free peoples maintain their free institutions" against the threat of "subjugation by armed minorities or by outside pressures." However, the tension leading to Cold War conditions had begun far earlier.
Shortly after the begin of the joint allied occupation of Berlin, General George Patton predicted that within a few years they (US and USSR) would be fighting for control of Berlin.
Some say it dated back to shortly after the US entry into World War II. In 1942, The United States and Britain decided to open their counter offensive by attacking German and Italian forces in Africa. Stalin wanted the US and Britain to invade occupied Europe, to take pressure off the Soviets, who were barely hanging on against Hitler's invasion.
Some even claim that it began in 1917, with the rise of Communism in Russia, and that the WWII cooperation between the Soviet Union and the West was a case of "Strange Bedfellows" against a very dangerous common enemy in Nazi Germany. After Hitler was defeated, the tensions that had existed before the war took over the relationship.
Most agree though, that the Cold War was on, beyond any doubt, in March 1947 with the Truman Doctrine; but there is strong argument to be made that the seeds for it were sown far earlier.
It started at the end of World War II when the Russians took Berlin. The Cold War was due to a rivalry between two allies during World War II. Through many different factors such as combat in the jungles of Vietnam, nuclear submarines, satellites in space and even factors within artistic expression helped to cause and spur on," the political and cultural war waged by Communists and Capitalists."
It is believe that the Cold War was hinted at near the end of World War II, and began at the Yalta Conference. When the Big Three (Churchill, Stalin, Roosevelt) met at the Yalta Conference, the tensions between the Western leaders and Stalin already existed. Stalin at that time had already occupied all of Eastern Europe, and to get the Soviets out would mean war. Soviet liberation of Eastern Europe was another form of tyranny. Stalin had control of the whole discussion, as Western propaganda hid the fact that Stalin was no better than Hitler from the public, because they needed to first defeat their common enemy, and because the United States wanted Russia's help to defeat the Japanese and the US also wanted Soviet support of the United Nations. So at the Yalta Conference, they were to discuss what is to happen to Europe after the war. They made "the Declaration of Liberated Europe" in which the nations themselves get to choose their own government. In the East, since the Soviets had set up provisional governments, Stalin agreed that after one year, they would hold elections. However, that would never happen, and sham elections that were held had voted the Communist party in power in each of the Soviet occupied countries. The Soviets did join the UN, but by then, it was clear that Stalin never intended to liberate Europe. Churchill is known for saying that an impenetrable "iron curtain" had fallen across Eastern Europe.