Scientific progress is talked about in three main ways, depending on the numbers/ proportion of the population involved in generating this progress:
1. Genius - 10s to 100s of people per generation – a fraction of 1 percent of the population.
Science is the product of a relatively small number of geniuses - without whom there would be no significant progress.
Therefore an age of scientific progress can be boiled down to the activity of tens or hundreds of geniuses; and the history of science is a list of great men.
2. Elite - 1000s to 10,000s of people per generation – a few percent of the population
Science is the product of an elite of highly educated and trained people, usually found in a relatively small number of elite and research-orientated institutions, linked in an intensely intercommunicating network. Without this elite, and these elite institutions, there would be no significant progress.
The history of science is a history of institutions.
3. Mass - 100,000s to millions of people per generation – a large percent of the population, most ideally.
Science is the product of a 'critical mass' of scientifically orientated and educated people spread across a nation or culture; and whose attitudes and various skills add or synergize to generate scientific progress. If society is not sufficiently 'scientific' in this sense, then there will not be significant progress.
The history of science is a history of gradual transformation of populations - mainly by educational reform.
A (common) twist on this is the idea that humans have vast untapped potential - and that this potential might somehow be activated - e.g. by the right kind of education; leading to an elite of geniuses, or a mass-elite, or something...
Perhaps the mainstream idea nowadays is a mushy kind of belief/ aspiration that science is essentially elite but that the elite can be expanded indefinitely by education and increased professionalization.
Another variant is that scientific progress began as based on genius, then became elite-driven, and nowadays is a mass ('democratic') movement: however, this is merely a non-historical description of what has actually happened (more or less) - underpinned by the assumption that scientific progress has indeed been maintained.
But I do not accept that assumption of continued progress (given the vastly increased level and pervasiveness of hype and dishonesty in science).
Certainly there seem to be historical examples of scientific progress without need for a prior scientific mass of the population, or even a pre-existing elite gathered in elite institutions.
Of course, nowadays there are no geniuses in science, so admitting that genius is necessary to significant scientific progress entails admitting that we are not making progress.
Nonetheless, my reading of the history of science is that a sufficient supply of genius is necessary to significant scientific progress (although history has not always recorded the identities of the presumed geniuses) – at any rate, science has often made significant progress without elites in the modern sense, and elites often fail to make progress.