There are many things that could be identified as key moments during this time.  Some of the most important include:

• The Marshall Plan
• The Truman Doctrine
• Churchill's "Iron Curtain" speech
• The Soviet Union's development of an atomic bomb  
• The communist victory in the Chinese Civil War
• The Korean War
• The Berlin blockade and the Berlin Airlift
• The building of the Berlin Wall
• The uprising in Hungary and the Soviet crushing of that uprising
• The creation of NATO and the Warsaw Pact
• The overthrows of Mossadegh in Iran and Arbenz in Guatemala
• The French defeat in Vietnam and the beginnings of a US presence there

These are only a few of the many possible key moments from the early stages of the Cold War.