The Long Telegram which in 1946 was a telegram from the secretary of state to the President of the USA talks about the after war years and the predictions/actions that the USA should take in a post Nazi world.

In it the predominant issue is communism, more specifically Stalin's communism which in their eyes was an expansionist ideology. This meant that the US advisers figured that the USSR would seek to expand its borders and slowly attempt to take over the world due to the difference in ideology of the rest of the world.

They then figured that it would be best to embark on a process of "containment" where they would try to contain communism by actively and passively combating communist sympathizers.

So basically the Americans figured that the USSR would seek to aggressively expand and ramped up military spending to counter it.

Note the Russian equivalent said the same thing about the USA and how the US would seek to destroy communism so they best expand first.

I'm not sure I agree with the underestimating to exaggerating, because from the beginning the US exaggerated the Soviet threat.

The Cold War was a tragic event that was started by mutual distrust.

On the one hand. After the Communist Revolution in 1917, Britain, France, US, and Japan sent troops to Russia to try to overthrow the Revolution. So the Soviets had good reason to distrust the "capitalist" countries.

Western powers give up in 1920, Japan finally leaves in 1922.

Then they sign an anti-fascist alliance with Britain and the US in 1941. But they find out that the US and Britain are making a superbomb (the nuclear bomb) without sharing any of the secrets with the Soviet Union. And that superbomb turns out to be huge.

On the other hand. The Soviet Union recruits sympathizers in every major foreign country and turns them into spies in the 1920s and 1930s.

The US goes into an anti-fascist alliance with the Soviet Union in 1941. This policy is urged by Soviet spies in US state and treasury departments.

The Soviet Union continues to send spies to the US, an ally. (That's how they know about the secret project to make the nuclear bomb.) These Soviet spies send back enough information that the Soviet Union explodes a nuclear bomb in 1949.

The US thought the Soviet Union was a reliable and trustworthy ally. But the Soviets break their word and do not allow free elections in Eastern Europe after 1945.

Soviet activity sparks the famous "Containment" memo of George Kennan in 1946 as posted above.

Truman doctrine of 1947 makes Containment official.

In 1949 Communists take over China and in 1950 the Communists in North Korea invade South Korea. Seems to prove the anti-Communists' point that the Communists are out to conquer the world.

3 line origin of Cold War: (a) Soviets were suspicious of capitalist countries from beginning (b) US felt betrayed after kinda trusting Soviets in 1941-1945 (c) Both sides say to people in their own countries, "See! Those bastards can't be trusted!"