Truman made a serious effort to have atomic weapons outlawed in 1946, and control of atomic energy passed to an international agency under the UN. The effort foundered - the USSR demanded that the weapons be outlawed and eliminated before any agreement on inspections and control was reached, while the US insisted on a phased elimination as inspections came into place. But those few months of negotiations were the closest the world has ever come to nuclear disarmament since Trinity.
It seems like some kind of compromise should have been possible - perhaps the US could be permitted to keep a stock of unmachined plutonium during the phase-in period, for example, under the guard of an international commission. The reason this wasn't reached was because, fundamentally, the USSR did not trust the US, and the US did not trust the USSR.
How could we avoid this distrust? I'm not really sure. Eliminating Stalin in favor of Beria is probably the simplest way, although that also has huge implications for Soviet domestic politics, probably leading to de facto decommunization in the 50s. Actually, replacing Stalin with pretty much anybody else would be a good start. It might also be possible to do something with American politics to smooth the path, but I'm not sure what.
If this did occur, that doesn't mean the US and the USSR are friends. They probably don't much like each other, and they're still going to be competing for influence and control around the globe. And it's regrettably plausible that the system might break down after it had been put in place. But, without the shadow of Armageddon hanging over everyone's heads, there's at least a chance for a world where the superpowers are rivals but not enemies.