Option 1:
Stalin decides that America is unwilling to use up its atomic stockpile in the defence of Western Europe. The Soviet Union takes advantage of the close timing of elections in Czechoslovakia, Italy, and France to declare that the diabolical Americans are manipulating the vote to prevent communist victories and Soviet troops must liberate Western Europe. No Cold War develops, because the world is now in the grips of the Hot War.
Option2:
Step One: Edward Benes refuses to accept the resignations of the non-communist ministers in the Czechoslovak government; the Communist Party effort to purge the police of non-communist elements is halted, but the Communist Party ministers are not punished for their effort. Stalin can see that the communist position in Czechoslovakia remains relatively secure, so the February Coup does not occur.
Step Two: The US congress continues to fight over the proposed Marshall Plan. It eventually passes, but with the Soviet threat somewhat less threatening, Marshall and Truman are forced to accept major cuts and the whole plan is smaller than either the initial proposals or OTL's Marshall Plan by a significant extent.
Step Three: European nations, especially Britain and France, are bitterly disappointed by America's stinginess, and retaliate by diplomatically protesting against the creation of a West German government. This doesn't prevent the functional creation of West Germany, but it both angers the Americans, thereby butterflying NATO as we know it. Meanwhile, the Europe-US split is obvious enough that Stalin is tempted to attempt to further the split diplomatically, and the Soviet Union begins increasing diplomatic efforts to appeal to Western European leaders.
Step Four: the Tito-Stalin split begins slightly earlier in the year (perhaps Tito feels Stalin is to collaborationist with the West?) and Stalin doesn't just privately denounce the Greek uprising by ELAS as overly confrontational with the West (as he reportedly did OTL, if you believe Yugoslav accounts[1]) but publicly calls for peace in Greece and the embrace of democratic means to end the conflict.
Step Five: Embracing his newfound role of peacemaker (so long as peace suits him) Stalin follows up by trying to halt Mao's advance at the Yangtze and encourage negotiations between Mao and Chiang. (As he reportedly tried to convince Mao to do privately OTL[2], but publicly). Whether this causes a serious enough split in the CCP to somehow get the KMT back in the game, or whether it only generates an extremely early Sino-Soviet split with Mao denouncing Stalin(!) a new player is added to the board and American fears about Communist dominance in Asia are suddenly vying with American hopes of encouraging an intra-communist civil war. (If you want to prevent the Cold War in the average American's mind establishing some kind of hybrid-coalition government in China would have huge effects, but its extremely implausible. An early Sino-Soviet split would have less impact on American political thought, but would still undermine a lot of the basis for rising tensions while also being somewhat more plausible.)
Step Six: Eduardo Chibas wins the Cuban election of 1948, begins an anticorruption drive, and gains support from the US State Department with promises of a better Cuba. He obviously can't solve all of Cuba's problems, but his efforts to clean up military corruption combined with the CIA warning Batista against a coup (since Chibas is popular in Washington) means that Cuba will never be quite destabilized enough for Castro's revolution to succeed.
There you go. Six major events which could have occurred in 1948 which collectively increase the belief in ordinary citizens of Western democracies that UN peacemaking can work (since Stalin seems to be supporting it) and that the American heartland is not at risk of communist subversion (since communist expansion will seem much more limited iTTL). The average Soviet citizen will still be told by their propaganda that they're besieged by Western imperialists, but a one-sided competition that forms only part of a multilateral competition should be quite different from our 'Cold War'. (Unless economics wins out, everyone ends up needing to decide whether they're going to suck up to the US or the Soviet Union anyway, and the fundamental Cold War lines just end up being drawn a few years later once the Soviet Union develops nukes. But I hope its at least plausible that something different- a four way atomic race with Western Europe and later China as distinct players- could happen.)
I should note that although the confrontation between the Soviet Union and the United States would look almost unrecognizable in this TL, and might well never get named the 'Cold War', there would certainly still be American efforts to diplomatically and economically isolate the Soviet Union, and Soviet efforts to spread communism abroad and maintain a repressive regime at home, not to mention espionage and military build-ups on both sides. The line between uneasy co-existence of two opposed ideologies and a Cold War is a blurry one, and this TL could tip over it at any moment (or even all the way to a hot war, if someone does something stupid at the wrong time); but at the very least tensions iTTL will tend to be quadrilateral (with the Soviet Union, the United States, Western Europe, and China all significant independent power blocs).
[1]Specifically Milovan Djilas' Conversations with Stalin. Note that Djilas is an unreliable source for OTL history given his Yugoslav bias, but even if Stalin OTL never believed this, he might find it convenient to embrace it in an ATL both as a diplomatic ploy and as a weapon aimed at making Tito appear a warmonger.
[2]Again, this is a highly disputed claim about Stalin OTL. However, he had at least been willing to back the KMT against Japan even when the CCP did not wish to be in a United Front, and his dislike of Mao as overly independent is somewhat more established.