Lets go through the list. Subsequently i will count not only USSR and US, but their allies, e.g. China, France, UK, Germany too:

https://en.wikipedia.org/wiki/Chinese_Civil_War

In the last month of World War II in East Asia, Soviet forces launched the huge Manchurian Strategic Offensive Operation against the Japanese Kwantung Army in Manchuria and along the Chinese-Mongolian border.[71] This operation destroyed the Kwantung Army in just three weeks and left the USSR occupying all of Manchuria by the end of the war in a total power vacuum of local Chinese forces. Consequently, the 700,000 Japanese troops stationed in the region surrendered. Later in the year Chiang Kai-shek realized that he lacked the resources to prevent a CCP takeover of Manchuria following the scheduled Soviet departure.[72] He therefore made a deal with the Soviets to delay their withdrawal until he had moved enough of his best-trained men and modern materiel into the region. However, the Soviets refused permission for the Nationalist troops to traverse its territory and spent the extra time systematically dismantling the extensive Manchurian industrial base (worth up to $2 billion) and shipping it back to their war-ravaged country.[72] KMT troops were then airlifted by the US to occupy key cities in North China, while the countryside was already dominated by the CCP. On 15 November 1945, the KMT began a campaign to prevent the CCP from strengthening its already strong base.[73] At the same time, however, the return of the KMT also brought widespread graft and corruption, with an OSS officer remarking that the only winners were the Communists.[74]

I’d say that is 50:50 USSR was there first to fight off the Japanese. When the USSR didn’t let the nationalists reclaim the territory, the US joined on the nationalists side.

https://en.wikipedia.org/wiki/Iran_crisis_of_1946

In the aftermath of the occupation of Iran, those Allied forces agreed to withdraw from Iran within six months after the cessation of hostilities.[6] However, when this deadline came in early 1946, the Soviets, under Joseph Stalin, remained in Iran. Soon, the alliance of the Kurdish and People’s Azerbaijani forces, supported in arms and training by the Soviet Union, engaged in fighting with Iranian forces,[1] resulting in a total of 2,000 casualties. Negotiation by Iranian premier Ahmad Qavam and diplomatic pressure on the Soviets by the United States eventually led to Soviet withdrawal and dissolution of the separatist Azerbaijani and Kurdish states.

That one is on the USSR

https://en.wikipedia.org/wiki/Greek_Civil_War

The conflict, which erupted shortly after the end of World War II, consisted of a Communist-led uprising against the established government of the Kingdom of Greece.

Note that the “Kingdom of Greece” government was a Fascist puppet of occupying Germany and Italy.

German forces withdrew on 12 October 1944, and the government in exile returned to Athens. After the German withdrawal, the EAM-ELAS guerrilla army effectively controlled most of Greece, but its leaders were reluctant to take control of the country, as they knew that Stalin had agreed that Greece would be in the British sphere of influence after the war. Tensions between the British-backed Papandreou and EAM, especially over the issue of disarmament of the various armed groups, leading to the resignation of the latter’s ministers from the government.

The Yugoslav and Albanian Communist governments supported the DSE fighters, but the Soviet Union remained ambivalent.[

The Greek Army now numbered about 90,000 men and was gradually being put on a more professional footing. The task of re-equipping and training the army had been carried out by its fellow Western Allies. By early 1947, however, Britain, which had spent £85 million in Greece since 1944, could no longer afford this burden. US President Harry S. Truman announced that the United States would step in to support the Greek government against Communist pressure. That began a long and troubled relationship between Greece and the United States. For several decades to come, the US

Stalin explained to the Yugoslav delegation that the situation in Greece had always been different from the one in Yugoslavia because the US and Britain would “never permit [Greece] to break off their lines of communication in the Mediterranean”. (Stalin used the word svernut, Russian for “fold up”, to express what the Greek Communists should do.) Churchill and Stalin had agreed in 1944 that Greece would be in the British zone of influence and Romania in the Soviet zone of influence.

That one is on the US and UK

First Indochina war doesn’t even list the USSR or China as involved. That one is clearly on the US and France

Paraguyan civil war again doesn’t even list USSR or China and is a US war

Malayan emergency, same thing. No USSR or China, but US involvement

Korean war - 50:50 as US and USSR split Korea in half, which let to the war

Mau Mau uprising - only UK is mentioned

Second Indochina war (Vietnam war) - that one is on the US and to a lesser extent France who also mainly destroyed South Vietnam instead of fighting for control in the North

First Taiwan Strait crisis - That one is not a proxy war from the Chinese perspective, as it is the continuation of the Civil War. With the US involving itself it is a proxy war on the side of the US

First Sudanese civil war - here the cold war opponents were on the same side with non combat support. Doesn’t make sense to count it imo.

Suez Crisis - Obviously on the UK, France and Israel who wanted to keep their colonial control

Second Taiwan Strait crisis - same as before. PRC China is not a proxy in its own civil war. The US has been using ROC as proxy.

1958 Lebanon crisis - US proxy war as USSR and China not even on the list

1959 Tibetan uprising - same as the Taiwan Strait crisis. PRC China is not a proxy on its own soil, that one is on the US

I will stop here, because i need to work. I’ll count Afghanistan towards the USSR as instigator into the proxy.

That leaves by my count (excluding the 6 or so more on that list) 4 proxy wars in which the Communist bloc was instigating or equally responsible. The Western bloc meanwhile has been instigating or was equally responsible in 13 proxy wars.