There was: “It, The Terror from Beyond Space” from the late 1950’s and “Planet of the Vampires” from the mid-60’s.
But most importantly, “Alien” kicked off a whole new aesthetic for outer space, spacecraft and alien monsters. This was picked up with gusto by lower budgeted imitators and knockoffs. The Italian film industry went wild with it (as they do with all successful genre films).
Arguably Forbidden Planet and 2001: A Space Odyssey were both space horror – I mean, they sure weren’t space romcoms or space heist movies. If you want to say Alien was the first space horror film with sexy black latex monsters bursting out of people’s chests, or the first space slasher film where everybody dies except a well-defined “final girl,” then yeah, probably, but we’d have to do research even to be sure about those two. “Horrible shit happens in space” is pretty normal for stories about space.