SWAT seems like it may have first been used in 1964 in response to bank robberies in Philedelphia, but it was popularized through LAPD developing it in response to the WATTS race riots of 1965.
"Early police powers and tactics used by SWAT teams were aided by legislation passed in 1967-8 with the help of Republican House representative Donald Santarelli. The legislation was promoted within the context of fears over the Civil Rights Movement, race riots, the Black Panthers , and an emerging War on Drugs."- (Balko 2013)
Balko, Radley (2013). Rise of the Warrior Cop: The Militarization of America's Police Forces. PublicAffairs. Retrieved 30 November 2014.