The two sides did not really do that much to sincerely try to avoid a Cold War. However, there were some things that can be taken as attempts to do so.
Mainly, there were attempts at making deals and creating institutions that would reduce the tensions between the US and the Soviets. For example, the Yalta Conference was to have settled the division of Europe in a way that would avoid conflict. The creation of the UN can be seen in this way as well. So can the creation of the IMF and the World Bank (though the Soviets refused to participate in those, just as they refused Marshall Plan aid).
There were, then, attempts to prevent conflict, but they were not that strong of attempts and they essentially came to nothing.