Alcohol was invented by microorganisms, of which the best known is yeast, many hundreds of millions of years ago. These little creatures consume sugars and produce ethanol as a byproduct. Now whenever humans had enough on the ball to gather fruit or grains in quantity, our friendly saccharomyces cerevisiae (the yeast that we use to make beer and bread) was there too, and always a party kind of microbe, started downing sugars and peeing out ethanol. Early man, ever frugal, did not waste the fermented brew and promptly got drunk. This would have indeed been a neolithic event.
Beer may have built the pyramids, because they certainly had it, as records from that time indicate the Egyptians imbibed. There is a serious academic hypothesis that beer made the long hard work of construction bearable. No one knows for sure who did it first, as it happened long before recorded history, but the discovery must have happened in warmer climates that microbes like, and probably by many people at many different times.