no specific date given but it is believed to be from April/May 1860. discovered by Firstsounds.org the person you hear is a french man by the name of Édouard-Léon Scott de Martinville. this might sound spooky to people who can speak french.
There's also a voice recording, dated 1885, of Alexander Graham Bell, the inventor of the telephone...This was converted from the wax discs of the era into playable audio files...Anyways, this is the voice of the man who created the birth of telephones.