The Great Seal of the United States was designed over six years by three successive committees. An eye in a triangle was proposed in the first of them, in 1776, on the suggestion of Pierre Eugene du Simitiere, a Swiss-born artist engaged as a consultant because the committee had no heraldic knowledge of its own. The final design was assembled in 1782 by Charles Thomson, Secretary of Congress, and adopted on 20 June that year. The reverse carries an unfinished pyramid of thirteen courses with the eye above it, and the mottoes Annuit Coeptis, he has favoured our undertakings, and Novus Ordo Seclorum, a new order of the ages. Thomson's explanation, submitted to Congress with the design, glosses the eye as the frequent interpositions of providence in favour of the American cause. That is conventional eighteenth-century Christian providentialism and nobody at the time found it remarkable.
Freemasonry did take up an all-seeing eye, and the earliest clearly documented Masonic use is 1797, in Thomas Smith Webb's Freemason's Monitor, fifteen years after the seal. Both drew on the same church-ceiling stock, which by then had been available for two centuries. Only a minority of the men on the seal committees were Masons, and du Simitiere, who introduced the eye, was not among them. That the two emblems resemble each other is a fact about a shared source, not evidence of a shared author.
The reverse of the seal was little seen for a century and a half. It went onto the one-dollar bill in 1935, at the urging of Agriculture Secretary Henry Wallace and with Roosevelt's approval, and that is when it entered general circulation and general suspicion.
The conspiracy literature is a genre with a documented history and can be described as one. It begins in the 1790s with the Abbe Barruel and John Robison, who explained the French Revolution as the work of the Bavarian Illuminati, a real society founded at Ingolstadt in 1776 and suppressed by the Elector of Bavaria within about a decade, whose actual size and lifespan cannot carry the weight put on them. The Illuminati did not use this symbol. The nineteenth century contributed the Taxil hoax, which its author publicly confessed as a fabrication in 1897 and which is still quoted; the twentieth added the John Birch Society's reading of Novus Ordo Seclorum as an announcement of world government; and the internet era has produced an enormous body of video and image material in which the eye stands for whatever the maker most fears. None of that is a reason to avoid the symbol or to treat the anxiety as unintelligible. It is a reason to be able to say plainly when the device was made, by whom, and out of what.