There were mass killings before 1968, but they were usually labor conflicts, gang warfare, and race riots. There was a school bombing in Michigan in 1927 by a man who was probably deranged. There was a massacre of 13 people in New Jersey. Within one month in 1966, there were the Richard Speck murders of eight nurses in Chicago and the Charles Whitman killings from the University of Texas tower. The Speck and Whitman crimes were the beginning of the wave of mass murders continuing to this day.
I am going by this from Smithsonian. Mass murders in the past were mostly organized crime fighting over turf.
https://www.smithsonianmag.com/history/story-first-mass-murder-us-history-180956927/
First school massacre was the Enoch Brown massacre in 1764 Pennsylvania.
https://pabook.libraries.psu.edu/literary-cultural-heritage-map-pa/feature-articles/enoch-brown-massacre-unmatched
Another happened in Hamilton TX in 1867.
https://texasescapes.com/TexasPersonalities/Ann-Whitney.htm