The NSA was spying as far back as 1919 in its precursory guise as Black Chamber. The Black Chamber persuaded Western Union and several other telegram and communications companies to give them illegal access to the telegram traffic of foreign embassies and consulates.
It’s difficult to know exactly when the NSA started the modern mass surveillance of American citizens. The public first became aware of this mass surveillance in late 2005 following a series of news reports. Thanks to these reports and evidence provided by whistleblower Mark Klein, a former AT&T technician, we know that the NSA has been spying on ordinary Americans since at least 2001.