The ice cream sundae emerged in the late 1890s and became extremely popular around the turn of the century. This popularity was substantially aided by laws prohibiting the sale of sodas on Sunday, and for this reason the concoction was first known as the "Sunday" or the "Soda-less Soda." The more elegant -ae ending probably came about when those who orated from the pulpit on the sinful soda went to work on the sacrilegious use of the name of the Sabbath for its stand-in.
As for the specific birthplace of the dish, two possibilities emerge as the most likely among many contenders. Neither place can offer conclusive dates, so one can pick between "Heavenston" (favored by the National Dairy Council, among others) and Two Rivers (championed by such diverse sources as the old Ice Cream Review and H. L. Mencken in his American Language).
The first claim goes back to the 1890s in Evanston, Illinois (then widely known as "Chicago's Heaven" or "Heavenston"), where civic piety had reached such a state that it became the first "Sunday Soda Menace." This prompted confectioners to create Sundays so that they could do business on the Sabbath. Ironically the soda was later given a strong boost from this community when the Evanston-based Women's Christian Temperance Union (WCTU) championed it as a pleasant alternative to alcoholic drinks.
The Two Rivers, Wisconsin, claim goes back to the same era and, so the story goes, was created when a youth named George Hallauer went into Ed Berner's soda fountain for a dish of ice cream.
