The problem with picking any specific period when some great transformational events occurred is that we’re on a path of exponentially faster change, a change that’s fueled by the corresponding exponential growth of knowledge and technology. So while you can pick a period where some really foundational changes occurred, there’s always another period just a little later when even bigger things happened.
For example:
One might say that one such major event was the spread of the first species of humans, the predecessors of homo sapiens, from Africa to Europe, the Middle East, and Asia. Yet these species, who were for practical purposes much like us, achieved nothing much else for two million years except the development of primitive tools.
Or one might say it was 12,000 years ago with the domestication of animals and the development of agriculture and permanent settlements. Surely that was transformational!
Yes, it was, but we had to wait more than 11,500 more years – until roughly the period 1500-1600, for the first glimmerings of what became the scientific revolution. Maybe that was it.
But just a few hundred years later – just 200 years ago, practically yesterday in the large scheme of things – was the first time that scientific advancement had a huge and absolutely transformative impact on the whole of society, by enabling the industrial revolution.
Since then we’ve had the information revolution and the advancement of technology in such leaps and bounds that new wonders are occurring every few years and society is being transformed and re-transformed faster than we can track the changes. On January 13, 1920 the New York Times ridiculed the idea that a rocket engine could work in the vacuum of space; 50 years later we walked on the moon, and the planet itself ceased to be the limit of the human domain. Today we have virtually all the information in the world at our fingertips, we’re surrounded by robots of one sort or another, and have sent them to every planet in the solar system.
In short, I think what makes the question difficult to answer is that the best answer now to when the world has changed most dramatically is almost always going to be “the last 25 years”, with that critical time period perhaps getting shorter and shorter as we move forward, some of the changes increasingly more dramatic.