The 42nd Street Library was inaugurated with a dedication by President William Howard Taft in front of 15,000 people on May 23rd, 1911. It wasn't until the following day, May 24, that the Library opened to the public, and stayed open for 13 hours, 9:00 am to 10 pm, welcoming more than 50,000 visitors. At the time, the building - which took 16 years to design and complete - was the largest marble building in the U.S.
The first book requested from the main stacks was Delia Bacon's Philosophy of the Plays of Shakespeare Unfolded. The book, much to the staff's chagrin, was not in the catalog and a staff member donated the book two days afterward. Fifty years later it was discovered that the interchange had been a setup; the staff member had hoped to generate publicity for the book. The first book to successfully be delivered from the main stacks, a speedy seven minutes after the call slip was deposited, was Nravstvennye idealy nashego vremeni (Moral ideas of our time: Friedrich Nietzsche and Leo Tolstoy) by Nikolai I. Grot.
Image source: "LIBRARY TRICKED ON FIRST REQUEST" New York Times (1923-), May 26, 1961 via New York Times (1851-2017) w/ Index
Opening Day in fact was the second time the public was invited to the Library. The first event was in March of 1911 when a wake was held in the third floor Rotunda for John Carrère who had passed away following a taxi cab accident. This is detailed in the New York Times article below:
Hon. John Bigelow arriving at the opening of Central Building from Digital Collections
From the "New York City — New York Public Library" Folder in the Picture Collection
From the "New York City — New York Public Library" Folder in the Picture Collection