In My Favorite Martian, September 29, 1963 to May 1, 1966, Uncle Martin's antennae might be either biological or mechanical, making him a cyborg with implanted mechanical parts, as far as I can tell from the photo in Turbo's answer and other images I found online. If antennae are cyborg parts opinions may vary whether Martians should be counted as a species with antennae.
In the The Outer Limits episode "The Zanti Misfits", December 30, 1963, the Zanti are about the size of rats, have six limbs, look like ants except for their human-like faces, and have antennae. They definitely count as aliens with antennae. But if being humanoid with antennae is necessary for the stock image of an alien with antennae, the Zanti don't count.
As far as I can tell, the Marians in Santa Claus Conquers the Martians, December 14, 1964, are never seen without their helmets. Thus their antennae seems likely to be parts of their helmets. It would be hard for people with antennae on their heads to put on helmets, trying to fit their antennae through the antenna holes in their helmets.
The Doctor Who tv serial "The Web Planet", 13 February 1965 to 20 March 1965, featured two insect like alien species, the butterfly like Menoptra and the ant like Zarbi. From online photos the Zarbi don't have antennae. The Menoptra do have clearly biological antennae and have a roughly humanoid body plan, except for their gauzy wings. So they may or may not count as the stock image of roughly humanoid aliens with antennea.
The Great Gazoo in The Flintstones first appeared in "The Great Gazoo" October 29, 1965. I haven't been able to find pictures of him without his helmet, so I suspect the antennae are part of his helmet.
I think that the first humanoid aliens with clearly biological antennae in movies and tv might have been Andorians in Star Trek, first seen in "Journey to Babel" November 17, 1967.
In the British film Quatermass and the Pit also known as Five million Years to Earth released September 29, 1967, the aliens have biological antennae, but they are insectoid, resembling grasshoppers. I don't know if they fit the image of humanoid aliens with with antennae.
The movie is based on the BBC tv serial Quatermass and the Pit, 22 December 1958 to 26 January 1959. According to Wikpedia:
Inside, Quatermass and the others find the remains of insect-like aliens resembling giant three-legged locusts, with stubby antennae on their heads giving the impression of horns.
So if the aliens from the BBC serial fit the requirements, they are the earliest movie or tv example so far. If they are not humanoid enough, the Andorians might be the first example.
I have seen many of the 1950s science fiction movies and I don't remember any with aliens with antennae.
So according to what I remember and can find out, the earliest aliens in movies and tv with antennae date to the 1950s or 1960s. The first aliens with antennae in such other media as comic books and science fiction literature might be much earlier.