I'd have to imagine that at some point in the almost two hundred years between when the US was formed and when the Cold War again, the two sides must have gotten mad at each other once or twice. But I don't remember hearing about anything major.
This seems to have been forgotten but the United States sent a Expeditionary Force known as Polar Bear Expedition into Russia to help quell the Red Forces along with a coalition of European nations and Japan to prevent Russia from turning Communist. Obviously the campaign failed and was plagued with problems. Logistically the coalition had problems sending fuel and arms because of naturally cold conditions in Russia. After the failed intervention relations and mutual paranoia about each nations intentions plagued US-USSR relations for many years.
Here is some back story on it:
The United States tried really hard to stay out of Europe's continental affairs, and was largely successful until WW1. Throughout the 19th century, after the end of the Napoleonic wars, Russia was an active player in the European balance of power system, along with Great Britain, France, Austria, Prussia, and to a lesser extent the other free German states (great discussion on these international balancing forces in Kissinger’s “Diplomacy” and “World Order”.
The US saw the damage of Europe's wars and wanted nothing to do with any of it. John Quincy Adams famously said "But she [the US] goes not abroad, in search of monsters to destroy" . Even the limited territorial wars of the mid to late 19th century (like the Crimean War, Russo-Turkish War, which Kissinger, Kennan, and Sluglett all write interesting accounts on) were on the same order of magnitude or larger than the American Civil War.
This changed somewhat with Theodore Roosevelt, who wanted to prevent Pacific region hegemony, and helped broker the peace treaty to the Russo-Japanese war (1905-1906). There was enough good will between the US and Tsar Nicholas II for Roosevelt to act as an (effective) neutral mediator at this time. This is what Kissinger writes about process in “World Order”
For Roosevelt, the issue was the balance of power in the Pacific, not flaws in Russia’s czarist autocracy…Because the unchecked eastward advance into Manchuria and Korea of Russia – a country that, in Roosevelt’s words, ‘pursued a policy of consistent opposition to us in the East, and of literally fathomless mendacity’ – was inimical to American interests, Roosevelt at first welcomed the Japanese military victories…But when the scale of Japan’s victories threatened to overwhelm the Russian position in Asia entirely, Roosevelt had second thoughts. Though he admired Japan’s modernization – and perhaps because of it – he began to treat an expansionist Japanese Empire as a potential threat ot the American Position in Southeast Asia and concluded that it might someday ‘make demands on [the] Hawaiin Islands’ (p. 252)
The stresses of WW1 pushed Russia over the edge and opened the power vacuum that let the Bolsheviks take power in the Communist revolution (Skocpol discusses how critical WW1 was as a tipping point for Russia’s Revolution in “States and Social Revolutions” ). This changed everything. While certain factions in America tried to pull back from international involvement after WW1, the underlying ideology of Communism required violent overthrow of capitalist societies. This led to the first [Red Scare of 1919-1920] (http://law2.umkc.edu/faculty/projects/ftrials/SaccoV/redscare.html), which was the fear that Communism would take hold in the US and lead to another revolution. So at this point, tensions were starting to develop between the US and, if not Russia directly, then at least Russia's communist ideology.
My background: I'm the co-host of the Reconsider Podcast, and we frequently do deep dives historical dives like this to provide research/context for contemporary political issues.
I actually just finished Jay Winik's The Great Upheaval, about the intertwined fates of America, Russia, and France. The US has had (or sometimes distinctly lacked) a relationship with Russia since its inception. In her youth, Catherine the Great admired the idea of liberal democracy, and eventually gained the title of the "liberal despot" in history. She begat a kind of renewal in St. Petersburg with the creation of beautiful architecture and replication of the French court and culture. When the Revolutionary War was brewing in the nascent US, she maintained a neutral stance, refused to aid Britain with military force or sanctions, and expanded trade through American ports. America and Russia both sought to take advantage of the other's resources. Catherine was interested in Britain and its former Colonies' resolution toward independence to secure a valuable trading partner.
But... once the democracy ball was rolling, the new European liberals of the middle classes took notice. The Enlightenment gripped the continent and eventually put a chokehold on the French government, also sparking off a failed revolt in Poland. Catherine during the French Revolution was expanding her empire by thousands of miles toward tantalizing warm-water ports south in the Ottoman Empire and didn't have the patience for peasant revolts and liberal sedition, so her attitude toward the US cooled. She frustrated the US ambassador by coolly refusing to speak to or even meet with him--for about two years--although they were in the same city.
So, the two nations were ideologically hostile, because Catherine as she aged became more imperialistic, and the US was [in]famously democratic.