The first major event was the Berlin Blockade and Airlift in 1948. Berlin was in the Soviet zone but was divided up (West and East).
Berlin divided into the four zones
The West (consisting of UK, USA, and France) introduced the new currency (the Deutschmark) into their zone, and the USSR responded by blocking food and other supplies into the Western controlled part of the city in order to get the other countries to allow a Soviet Union rule throughout. The West responded with the Berlin Airlift, dropping supplies into the city until Stalin realised that he was not going to win unless he turned it into a “hot war” (i.e. physically attacking the Western Allies with troops). He gave up but it was the first major event that turned the two sides against each other.
Over the next 35 years, the two sides would continue to threaten each other until it became all too much.