I should also mention Led Zeppelin. I think Led Zeppelin were the first band to take all of the heavy metal ideas that had been tried by others and put them all into one big monster sound. Zeppelin's drums were very loud in the mix and the screaming, moaning vocals of Plant were pure metal. Of course Janice Joplin was doing that sort of thing vocally as well as having a loud band, but Zep took it to the next level.
If you listen to Black Sabbath's early albums you can tell they borrowed a lot of ideas not just from Cream but also from Zeppelin. It's seldom mentioned how the main guitar riff in the Sabbath classic Paranoid is borrowed from the Yardbirds/Zeppelin classic Dazed And Confused.
You are absolutely right. Led Zeppelin, Deep Purple, and Black Sabbath all incorporated the sounds, lyrics, and styles we now call "metal" at about the same time. They all were born in 1968 !! Actually Black Sabbath wasn't truly born until 1969 and Deep Purple began touring in 1967 but called themselves Roundabout. Led Zeppelin originally began as "The New Yardbirds" but made a change to Led Zeppelin in late 1968. So who is the FIRST METAL BAND????
Led Zeppelin actually began their career borrowing from the Yardbirds, and didn't release their first album until 1969, and a large portion of this first album was acoustic.
Black Sabbath didn't actually become "Black Sabbath" until 1969, when they ditched the band name "Earth". It was with this name change to Black Sabbath that the band began writing metal music. Their first album was released in 1970, and they borrowed from Cream prior to their changes.
I think it is fair to say Deep Purple is the first true Metal band. They formed in 1966 and were back up for Cream. They began as the band Roundabout, but made a name change in the spring of 1968 to Deep Purple, and released their first album, "Shades of Deep Purple" in 1968.
Some will argue that Led Zeppelin and Deep Purple are hard rock, but I am with the millions who think they are metal. And I would definitely agree with the stats that say Black Sabbath is the first metal band if Black Sabbath didn't fit more into the category of the FIRST Death Metal/heavy metal band than the first metal band.