The Cold War was caused by several factors:
The nuclear rivalry - both sides' desire to obtain nuclear arsenal mixed with the American refusal to voluntarily share its nuclear progress with the Soviet Union.
Key ideological differences between western liberal-democratic capitalism and Soviet-style socialism, particularly communist belief in global revolution versus the capitalist belief in a global free market if not a global system of democratic states.
Soviet desire for a secure western border for its power bloc, especially regarding the city of Berlin.
US/UK desire for an expansion of the own economic sphere of profit and influence.
Opposed political goals in Germany, Korea, China, Vietnam, Afghanistan, Ethiopia, Angola and other zones of social strife.
So, while the refusal to share nuclear secrets is in fact "Truman's fault" and Truman's distrust of Joseph Stalin is perhaps a personality-driven factor in the early history of the cold war, just viewing the political situation through various lenses will tell us that the conflict is rooted deeper than in just the person of Harry Truman.
Viewed through a machiavellian lense, we have two states obsessed with power and supremacy over the other. Both countries discarded their own moral compasses at various points in time, with the United States aggressively intervening in political elections of supposedly free independent peoples like the Italians in 1948 (Truman) or the Chileans in 1973 (not Truman). Both sides were manipulating world events in their favor not only due to the favor of the other side doing the same but also to actively expand their own power structure on the global scene.
Viewed through a marxist lense, we might think at first glance to see a class struggle as described by Karl Marx, but the Cold War itself - the strife between USA and USSR - might not be as classist as one might be lead to assume. However, we do see class struggle as described by Marx in Vietnam, where communist militias overthrow the Japanese and French colonial lords and then fend off American and South Vietnamese influence. We do see the narrative of the class struggle in Italy and Chile, where communist or at least socialist parties have real chances of peacefully achieving a transition to socialist ideology - although the peaceful option had of course not been really considered as on the menu by Marx and especially not by Lenin.
We might also apply a keynesian lense to analyze the two sides' economic interests and internal financial workings, and once more we would come to the conclusion that the economic interests of the state, especially every little economic footnote attached to either side's military-industrial complex, was aching for a passive conflict between the two - the economic output of both sides were highly militaristic in a fashion that the aggregate demand of the populations simply were unable to cover.
I realize I am ranting at this point. What I am saying is that Harry Truman's decisions alone did not create the potential for conflict between the two sides. Too different were their goals and outlooks on the world - and these outlooks go back to the decisionmaking and personal philosophies of Engels, Marx, Smith, Jefferson, Hamilton and Washington just as much as they go back to the immediate actions of Harry Truman - and even if we indulge in Truman-bashing in such a way, mentioning that his direct counterpart Joseph Stalin was someone who had aggressively attacked Finland, Romania, Estonia, Latvia and Lithuania not even ten years before the actions we are discussing would be a necessity as well. Stalin was someone who could not be trusted, and blaming Truman for realizing that is not an honest look at history.