Often used to describe bands like Pantera and Exhorder. With mid-tempo riffs similar to those found in Thrash Metal and a tendency to focus more on groovy syncopation and heaviness than outright speed.
Yeah, the internet seems to think it's either them, or a punk band called the Germs from LA. This Lexicon Devil EP is from May '78 but they also had a single out in '77 that was maybe a little less hardcorish. As with any new sub-genre it's hard to know exactly where to draw the line between what was punk and what was hardcore. I'm sure there were other bands in the mix as well that have been largely forgotten because they just didn't get any recordings out there. I was in high school from '76 to '79 and I wasn't aware of any of these bands at the time, I only knew the Ramones, the Pistols, the Dead Boys and the Clash.
DC's Bad Brains formed in 1976, but I believe they were playing some kind of a jazz fusion at first going by the name of Mind Power and then switched to playing hardcore later, taking their name from the Ramones song Bad Brain (1978) Even though they wouldn't describe themselves as a hardcore band because they have wide ranging influences like jazz and raggae, I think most of the rest of the punk world considers them one of the earliest notable hardcore bands. But they did't get an album out til '82, and by that time hardcore was already a well established sub-genre.
The Germs - Lexicon Devil EP 1978
SS - Coca Cola, 1978 Japan Raw Hardcore Punk/Noise Punk. Then there were these guys SS briefly over in Japan who broke up in 1979.
The Clash - The Clash, UK 1977, first two Clash albums were better before they went all commercial. Not that I really mind their more commercial stuff.
The Clash - Give 'Em Enough Rope, 1978