I wrote up a reply to a now deleted comment which suggested 1700s (the Enlightenment period) and the Cold War as likely contenders, but I was too late to submit it. Instead I will post it as a reply to the OP (so don't mind the references to the now deleted post):

It is extremely difficult to gauge the extent of atheist/agnoistic or similar beliefs in history, because for most of history it has been forbidden and usually under threat of severe punishment to openly declare yourself as one. Also even though throughout history there have been times and countries of more or less religious freedom, we lack statistical information to make any solid assumptions even about the numbers of adherents to various faiths, much less about adherents of disbelief. In most instances we only really have the other side of the case, that is theists accusing other people, named or unnamed, of being atheists, and only very rarely any statements from atheists themselves. This has led some historians (not least Alan Charles Kors) to propose that atheist didn't really exist until the Early Modern period, where the first philosophers, due to a changed religious climate following the Reformation and the end of the Religious Wars of the 16th and 17th centuries, could relatively openly propose some form or other of irreligiosity. All earlier mentions of atheism was simply done for dialectic reasons, for theists to have an opposite of their belief in which they could apply their arguments for theism upon. This theory itself has been criticised, among other things for making assumptions from lack of sources, and academia still seems to be divided on the issue (for this discussion see the Introduction of Hunter & Wootton, 1992).

While there was a number of famous philosophers and other prominent people in the late 1700s that adhered to atheism or agnostic (however anachronistic that term is for the period) line of thought, they really only comprised a very small, and usually wealthy and privileged, part of the population of the Western world, and definitely does not compete with the numbers of atheists today (even though only very few Western countries does have atheist majorities today). Even amongst philosophers of the Enlightenment period, deism was far more widespread than atheism or agnosticism (see Jonathan Israel, The Radical Enlightenment, 2002). Even in Revolutionary France, which was arguably the country where, for various reasons, atheism was most widespread anywhere in the Early Modern period, and where for a short period of time complete religious freedom reigned, allowing those groups to openly declare their convictions, they never amounted to more than a small minority.

Sources:

• Michael Hunter and David Wootton (eds.), Atheism from the Reformation to the Enlightenment, Clarendon Press, Oxford, 1992.
• Alan Charles Kors, Atheism in France, 1650-1729, Volume 1, Princeton University Press, 2014 (originally published 1990).

You make a good point about the Soviet countries of the Cold War, but while these countries officially termed themselves atheist, we do know that religion still flourished clandestinely, this was also and of course has seen a revival in many of those countries following the end of the Cold War. Ironically here we experience the same effect as above, but with from the opposite end of the spectrum, that it is difficult to estimate the spread of religion because it was mostly forbidden to openly declare yourself a theist. As such for obvious reasons we lack solid and reliable source material about the spread of religion in Easter Bloc countries, and we can't really say exactly how many people where truly atheists and theists, and comparisons are thus very difficult to make.

However considering that studies show that religiosity is higher in percentage among the poor, and that global poverty is on the decline and probably never has been as low as it is today in the whole of human history (again lack of sources makes comparison for this in effect impossible) it seems likely that the number of irreligious people is higher now than at any other time in human history.

Followup Question:

I recently inherited a copy of Marcus Aurelius's Meditations printed in 1947 1945 from my grandparents. The author of the foreword claimed that, during the decline of paganism, educated Romans didn't turn to Christianity, but instead derived their morals and worldview from ancient Greek and contemporary philosophers. Is there any truth to the idea that middle and upper class Romans were predominantly non-theistic?

I'll edit this post when I get home and find out which historian wrote that foreword.

EDIT: The foreword was written by Irwin Edman.

The stately ceremonies and customs handed down from the past were still punctiliously and lavishly performed in public, as signs of gratitude to whatever had formerly made Rome great and as a means of impressing the multitude. But few educated or thinking men now took them seriously. Their minds had been trained from youth in the schools of Greek philosophy, and Plato, Aristotle, Epicurus, and the Stoic Zeno, each had his following. But now even the illustrious philosophers received the unquestioning veneration that once they had had... The Skeptics, who doubted that any philosopher ever had or ever could fathom the world's mystery, attracted many who scornfully refused to imagine certainties where none existed.

It seems as though he is suggesting that educated Romans under Aurelius not only doubted religious institutions, but any central dogma whatsoever.