For much of ancient history people always seemed to assume that 10 years, 100 years, and 500 years from when they lived would be more or less the same because technology was advancing too slowly for anyone to really notice. Many cultures even had the idea that times were getting worse as they moved further from a fictional "golden age."
So when did people start realizing that the future would be more "advanced" than their own time?
As it's been for a very long time we have seen the advancement of technology first and foremost in battles. The invention of gunpowder and it's use to make muskets, rockets, and cannons are probably the fastest change we saw in terms of change and advancement in warfare.
It wasn't really until the industrial evolution that things really escalated exponentially. Society wasn't just creating weapons it started also recreating ideas and concepts that were dreamt up by long dead scientists and mathematicians. Steam power, electricity, the concept of mass production, the rise of working class, and new social and economic policies going into effect really changed the world we live in.