January 30, 2000
To answer your question, a book by astologer/stock market scholar Bill Meridian (obviously a pen name) includes the first trade charts for hundreds of companies on the NYSE and NASDAQ. Companies which started trading earlier than July, 1985, are shown with 10:00 AM birthtimes; companies which began trading after that month are shown with 9:30 AM birthtimes. Dates are also given for a number of financial institutions. Specifically, the chart for NASDAQ gives a birthtime of 10:00 AM on 5 Feb '71. Hope this helps.
[Thanks to Tom Wuthrich for this update. -- Starcats]
1971: "Nasdaq celebrates its first official trading day on February 8th-the first day of operation for the completed NASDAQ automated system, which displays median quotes for more than 2500 over-the-counter securities."
New York Stock Exchange