During the Cold War era, the US had adopted the containment strategy, a foreign affairs approach which focused on stopping the spread of communism worldwide, that was already suceeding on the Eastern European regions where the URSS had managed to impose its influence sucessfully.
Directly attacking the URSS would have meant a nuclear war and the destruction of both the US and the communist bloc leaded by the URSS. This is why URSS and US fought indirectly by intervining in proxy wars (for example, Korea or Vietnam), where they supported opposite sides.
