A good working definition of the Cold War could go like this:
Competition between the Soviet Union and the United States over ideologies, through other countries, without direct armed conflict
As it became obvious that the Allies were going to win World War II, the "friendship" between the Russians and Americans began to fray. Both countries started to jockey for position in a postwar world. This emerging competition for control of foreign governments and systems, as well as resources, began the Cold War.
Armed communist rebellions began in Greece and Turkey in 1946. The US shipped weapons to put down the rebellions. The Soviet Union blockaded West Berlin in 1948, and the US responded with a year long airlift of supplies. The Western powers formed the NATO alliance for self defense. The Soviets responded with the Warsaw Pact. In 1949, the USSR developed its first nuclear weapon.
No one of these events started the Cold War, but in combination and rapid succession, it was inevitable.
Events in the 1950s:
Hydrogen Bomb and ICBMs developed
Guatemala intervention by the US
Hungarian Uprising crushed
Space race begins with Sputnik
Cuban communist revolution