why did the cold war start and when

The Cold War began shortly after the end of World War II in 1945. The reason the Cold War started was the the Soviet Union (Russia) violated international agreements about how war-torn Europe would be governed and rebuilt. One such agreement they violated was that territories recaptured from Germany would be given democratic elections. Instead of instituting democratic elections, the Russians set up what were essentially puppet communist governments controlled by the Soviet Union. Angered by this, the United States and the other western democracies refused to "appease" Russia as they had Germany prior to World War II. Instead, they instituted a policy of containment, in which they would not fight the Soviets directly but would seek to prevent them from expanding their territory and ideology into new places. This is why the United States fought several conflicts to promote democracy and prevent communism from spreading during the Cold War.
https://edsitement.neh.gov/curricula/origins-cold-war-1945-1949