I'd disagree with your assertion that there were no meaningful territorial, economic, or cultural disputes is inaccurate. The Cold War started in large part because of disputes over these exact issues.

Territorial disputes erupted over control of Eastern Europe after World War II. As the war wound down, the question of Poland's post war government took on increased significance. Poland was ostensibly the reason that Britain and France declared war on Germany in 1939 and it was the most prominent issue raised at the Yalta Conference. Churchill and Roosevelt wanted Stalin to allow the government in exile (residing in London) to take part in free and fair elections, which they would have likely won. Stalin had little desire to allow this, as he viewed control of Poland as essential to the security of the USSR. Germany had twice used it as a pathway to invade Russia, and Stalin wanted to ensure that any repeated effort would face a Soviet-controlled Poland that could in theory blunt any real attack. Soviet actions to ensure communist victory further enflamed tensions in the Grand Alliance. The Red Army slaughtered Polish army officers in the Katyn Forest and effectively purged anyone in the country that did not have ties to Soviet-backed communist groups. The violent, unlawful actions and rumors that the Red Army intentionally slowed its advance to prevent the success of the Warsaw Ghetto uprising poisoned relations between the allies. Similarly, the fate of other eastern European nations became a major issue in the post-WWII environment.

Economic conflict formed the heart of the conflict as both sides viewed the other's system as an existential threat. The United States' view for a post war environment depended on access to markets and a system of free trade. The Soviets wanted a closed system of exchange between communist nations. This reared its head most prominently during discussion of the Marshall Plan. The United States offered Marshall Plan aid to the Soviets and their satellites in Eastern Europe, betting that the control of the economy those nations would have to cede would prove unpalatable. George Keenan argued to Marshall that the offer was essential despite the risk of incurred cost, since it would then cast the Soviets as denying something desirable to their proxies. This assessment proved correct as the Soviet Union refused the aid and forbade Eastern European states from accepting it. Economic conflict also arose as soon as the war ended as the US immediately suspended lend-lease aid to the Soviets and refused their request for massive loans for reconstruction.

Cultural concerns also arose immediately as both sides had spent decades before WWII casting the other as an enemy. It took a herculean propaganda effort to create "Uncle" Joe during WWII and once this effort ended old suspicions reemerged. Anti-Communist materials began to dominate popular culture, notably in things like Mickey Spillane novels. Similarly, Soviet propaganda began downplaying the role of Britain and the US in winning the war, instead creating a narrative that centered on the Soviets doing it largely unassisted. Old themes of attacking the decadent west reemerged as a way to shore up the system, particularly given the obvious wealth and prosperity that the Red Army saw as they advanced into Germany.

TLDR: The Cold War emerged due to conflicting interests and objectives for the post-WWII world sparking significant territorial, economic, and cultural dispute.