The seeds of modernity trace to the beginning of Western Civilization, particularly to Greco-Romanism. The Greeks invented or discovered science. And Rome, at its peak, invented things like the aqueducts, so advanced for their time, that the world would not again see until close to the modern era. (This clip from "The Life of Brian" brilliantly pokes fun at pagan achievements at the expense of the early Judeo-Christians living in Rome.)
Still, when Rome went Christian, it was mainly the bright minds within the Roman Catholic Church who preserved the great knowledge of Greco-Roman antiquity and incorporated such into Christendom. One thinks of Aquinas' affinity for Aristotle.
But those seeds still didn't begin to grow into the tree of modernity until around 1800. For instance, as Cato's Encyclopedia of Libertarianism, in their chapter of "Material Progress," notes, if you compare the life of George Washington to Julius Caesar's in 44BC, you'd see that though Washington could take advantage of some notable material advances that didn't exist in Caeser's day, their material worlds were far closer to one another's than either are to today's modern technological world.
In other words, there was a watershed in technological progress. It began in the late 18th Century.
So what caused it? That's what Cato's Symposium debates.
My studies conclude it wasn't God, the Bible, Christianity or Thomism (after all, these had been around for a long time before the watershed, but may in fact have contributed to the information contained in the seeds). Rather it was a form of Enlightenment humanism that put the focus of socio-politics on man, his material (as opposed to spiritual) needs, and the "progress of the human mind," as Jefferson once termed it.
This isn't to say the Founders and the philosophers they followed, as scientifically minded, materialistically concerned people, were secret atheists or hostile to religion, as some have supposed. To the contrary, they tended to appreciate the way religion civilized man and made him self-governable which was indispensable to modern republican government. (America's Founders also believed that the states, and voluntary local institutions, should bear the primary if not sole responsibility for promoting the kind of religion useful to modern republican government.)
But, as America's Founders intended it, God and religion would not be the chief focus of the Novus Ordo Seclorum. Man's material needs would. One need look to the United States' original Constitution for evidence. Such is a document of limited, enumerated powers. And, whereas it endowes those things that relate to man's material concerns, the Constitution left religion unendowned. As Walter Berns put it:
[W]hereas…[the Constitution] grants Congress the power “to promote the Progress of Science and useful Arts” (see Article I, section 8), it nowhere gives it the power to promote religious belief. Rather, the First Amendment seems to deny it such a power. — “Making Patriots,” p. 43.
Also striking is how many key American Founders and the philosophers they followed were scientists, usually natural, in some formal or serious armchair way. For instance, Benjamin Rush was a medical doctor. Benjamin Franklin invented bi-focals and the lighting rod. Thomas Jefferson invented "the swivel chair, a pedometer, a machine to make fiber from hemp, a letter-copying machine, and the lazy susan." The Founders idolized such British figures as Isaac Newton (discoverer of gravity), John Locke (a medical doctor), Joseph Priestley (the co-discoverer of oxygen), all natural scientists, in addition to being other things. They also idolized men like Adam Smith (the father of the modern science of economics), and Richard Price (the father of the modern science of finance). Indeed morals, law and politics were all viewed as "sciences" of some sort -- part of the "the new science of man." Principles thereto were "discovered," not posited. And they believed sound governments could be built according to almost (if not literal) geometric principles.
Religion too, they believed, could be reduced to a rational science. They did not yet discover that God didn't exist (as some scientists have claimed to have discovered today). All of the above mentioned figures, I sincerely believe, devoutly believed in God's existence. However, their scientific rationalistic approach to religion (as to all other things) led most of them to doubt or deny the Trinity (1+1+1 = 3 not 1) and the infallibility of the Bible (those parts of the text that seemed most unbelievable according to a scientific perspective).
As it were, following the advice of scientifically minded Enlightenment philosophers, America was founded to be a scientific, commercial republic, one whose chief focus would be meeting man's material needs and wants. Such a system has been termed "liberal democracy."
Whatever one thinks of it, liberal democracy, in putting the focus of socio-politics on science and man's material needs, proved quite effective. It led to the astounding technological advances seen in the last two hundred years. And because those technological advances applied to military and economic power, liberal democracy in general, America in particular, came to dominate world geo-politics.
Such, as I understand it, is the story of modernity.