Impossible to say, due to the chaotic nature of historical causality and the fact that your question is horribly undefined to the point of being essentially meaningless. How, exactly, did the holocaust not happen in the alternative history we are here hypothesising? Due to the nature of causality, there are countless ways that the holocaust could or could not have happened in alternative chains of events, but my guess (based on almost totally inadequate understanding - anyone here sufficiently qualified in the relevant math and physics, feel free to tear me a new one) is that you can only cause forks in those chains at the uncertain, sub-molecular, quantum level - at the superquantum level, everything seems pretty much classically determinate and thus a depdendant, unchangeable variable except perhaps right at the very beginning of reality itself.
In order for there not to have been a holocaust, there might have been nothing more than a single atom that bounced a different way in some air current decades or even centuries earlier, that perhaps changed the course of some turbulent gust and carried a single germ into the lungs of some person who then became ill and stayed home on a day they otherwise wouldn't have done, perhaps not making his quota of shells in the munitions factory that day and changing the course of a battle due to a shortage of ammunition, and so on and so forth, events in turn spiralling and diverging from our reality ever more drastically until eventually whole wars didn't happen, or were won by the other side, or happened exactly the same way except a single battle was fought with cavalry instead of infantry, or whatever.
If that's too much of a stretch for you, here's a more direct one - perhaps the gust of wind changed by a single errant molecule caused the gas attack that, in our reality, temporarily blinded Hitler during the First World War to instead kill him outright. But if that happened, not only mightn't there have been a Holocaust or the Nazis, but Germany might very well have become Socialist - Socialism was extremely popular post WW1 in Germany, and had the Nazis not gained their charismatic leader and completely usurped them, they might have taken power instead. In turn, with Germany Socialist (and by the end of the inter-war years, one of the most advanced nations on the planet), the domino effect so feared by the US might actually have happened and Russian, Soviet-style Communism might well have spread across all of Europe by the '30s (or there might, say, have been a war between different Russian and German interpretations of Communism), which would have left all of modern history totally unrecognisable. There's countless ways history could have unfolded differently in the insanely wide scope of your question - if there had been no Holocaust because some random atom in someone at the Wannsee conference's brain jumped the other way that day, the Nazis themselves might even have decided it was a better idea to deport the Jews into Israel to get rid of them, rather than keeping them in Germany and wiping them out.
At some other, far removed branch of the tree of causality, there may never have been a Holocaust because there may never even have been any Jews - some dust mote bouncing around in the air might have bounced the other way and choked Moses at a crucial moment during an inspiring speech (assuming he and the relevant events existed as described, of course, which is a big fucking assumption), he never got his momentum back, the people lost faith in him and the Jews died out altogether, lost in the desert. Of course, such a crucial change so far back would also have left effectively all the history we know unrecognisable - no Jews -> no Christians -> pretty much all of history in Europe, North Africa and the Middle East, ancient and modern, totally different.
