Strained at best would be appropriate. Following the October 1917 Revolution the U.S. was one of the foreign "interventionists" who actually sent troops into Russia. Granted it was a small number and in/around Vladivostok, which had no effect on the outcome of the Russian Civil War, but this was certainly enough to alienate much of the Soviet leadership. The next major issue was the nature of Communism being (of course) explicitly anti-capitalist. Given the U.S's status as the preeminent capitalist country this was sure to rankle. There were additionally some attempts by the Soviets to form a cohesive American Communist Party that looked to Moscow for orders, but this largely failed. These attempts and general fears actually led to a period of "Red Scare" in the U.S. in the 20's. And the largest indicator of the relationship between the two states was the fact that it was not until 1933 and FDR's election that the United States formally recognized the USSR as a state. As to the second part of your question, the cooperation of the two countries during WWII can be seen as an aberration, of a marriage of convenience, than the rule. This is why the mistrust and fear of the Cold War was able to arise so quickly: because it had always existed to some degree. Adam Ulam's "Expansion and Coexistence" and Robert Services "Spies and Commissars" are both good sources on this topic.

/u/lupuswolfe has provided a good summary of the diplomatic sphere, where tensions were always present. That said, it's worth noting that that the Soviet view of the US was far from uniformly hostile. To borrow from an old comment, we should capturing some nuances here.

From the Soviet perspective, while America was obviously a capitalist power - and one that had intervened in the Russian Civil War - it was rarely considered to be at the forefront of the 'camp of hostile powers'. While Washington was occasionally considered to the 'boss of Europe', ie home of finance capital, in practice Moscow was much more concerned about events and relations in London, Berlin, Warsaw and Tokyo.

At the same time, America had many positive connotations in the USSR. Lenin had been a firm fan of Taylorism since before the Revolution and this theme was picked up by his heirs. To the Bolsheviks 'America' stood as a symbol of economic modernisation and technological advancement. Nor was this an elite concern: during the 1920s American cinema and fiction was very popular popular in the USSR, US-made machines were praised for their robustness and Henry Ford was the subject of a veritable peasant cult.

In short, the US was largely seen as the paragon of modernity, a society whose abundance and technological achievements were something to aspire to. To be a 'Soviet American' was to be efficient, energetic and get things done in pursuit of this vision. This fit particularly well with Stalin's industrialisation drive of the late 1920s.

This almost-admiration never existed apart from more critical voices of America (its race problems, foreign policy, etc) but while it existed it was a powerful modifier on Soviet views. However in the early 1930s, the Depression in America and the Soviet cultural turn inwards saw these positive themes disappear from the Soviet press. The negative critiques of the US thus came to dominate official discourse and policy. Ironically, this coincided with the official thawing of relations in 1933.

So while there were clearly fundamental differences between Washington and Moscow that made rapprochement difficult, I'd avoid the trap of viewing the Cold War simply as a continuation of a pre-war tension. Arguably there was a window in the 1920s for both nations to come to terms; nor were the differences between them of the same geopolitical character as in the post-war period.

Jeffrey Brooks has a really good essay on Soviet perceptions of 'America' in Russia in the Era of NEP.