I was playing call of duty cold war (obviously ficctional) where in some missions of the campaing and of course the multiplayer there are soviets and americans directly entering in combat whit each other, and a wondered if that actually happened at least once during the entire cold war, I know that could have ended up in a nuclear war, but what if there is an exception? Or something like that, in school I was taught that soviet union and USA never entered in combat with each other, but I also think that the cold war lasted for a very long time and during that time, something happened between them directly, I mean, the cold war was also a war full of secrets hidden by the governments, and they hated each other's a lot. So that's it
It was pretty common for Soviet and American air forces to clash during the Korean War. Oftentimes, the Soviet pilots would be operating "in secret" so as not to provoke the UN. This would include flying in Chinese or North Korean marked aircraft and uniforms, although radio interceptions would reveal the pilots were speaking in Russian and flying under the guidance of Soviet ground controllers. Eventually, after the end of the Cold War, Russia declassified their involvement in the Korean War. Some notable examples of this you could look into include MiG Alley and the aces Nikolai Sutyagin and Yevgeny Pepelyaev.
It is highly suspected Soviet pilots were involved in combat during the Vietnam war as well. However, this topic is much less researched, with only Vadim Shchbakov being credited with any kills as per declassified documents. However, many Soviet soldiers did operate Air Defense Batteries, with it also being confirmed after the Cold War that entire SAM units would be operated by Soviet soldiers in NVA employment. Source: U.S.-Russian Joint Commission On POW/MIAs, 23 April 1993
As far as I know, in terms of ground combat, there have been no Soviet-US engagements. While it's certainly possible, with the large numbers of "instructors, technical advisors and military experts" that would be deployed by both the US and the Soviet Union, there's no hard evidence to support it.