Besides physical contact, another form of contact is telepathic. This also has an old history. People have been claiming to receive messages from supernatural entities for centuries, and likely for as long as humanity has existed. Messages from gods and angels and ghosts and saints and the like. The recipients of these messages have received them in several ways. Voices in the head. Speaking in a trance. Writing in a similar fashion (automatic writing). Pointing out letters (Ouija boards and the like). This activity has gone under various names, like necromancy and spiritualism and channeling.
But let's back up a bit.
Supernatural entities are at least partially independent of the physical Universe, while extraterrestrial sentient entities (ET's) are entities like us, which inhabit the physical Universe, and whose ultimate nature is mostly or completely physical. I saw "mostly" to include mind-body dualism.
Speculations about ET's are almost as old as speculations about the existence of other Earthlike objects in the Universe, if this quote from Democritus (460 - 370 BCE) is any guide:
In some worlds there is no Sun and Moon, in others they are larger than in our world, and in others more numerous. In some parts there are more worlds, in others fewer (...); in some parts they are arising, in others failing. There are some worlds devoid of living creatures or plants or any moisture.
A "world" here is a Ptolemaic cosmology, with an Earthlike object in the center and suns, moons, planets, and stars orbiting it. The Epicureans also believed in this cosmology, though most of their fellow philosophers believed that there is only one world, by this definition of a world.
The next step forward was over a millennium later, when Galileo started looking at celestial objects with his telescope. The Moon already seemed vaguely like some other world, with its round shape and its blotches, but Galileo saw lots and lots of mountains on it. It was evident that the Moon is much more Earthlike that anyone had ever thought. He could not resolve the other planets very well, but he saw spots on the Sun, phases of Venus, the four biggest moons of Jupiter, and something or other around Saturn.
It was evident that the other planets were worlds like the Earth, and by the 18th cy., it was very commonly believed that ET's were living on most or all of them. But nobody claimed to have visited them until Emanuel Swedenborg (1688-1772). He was a scientist who started getting religious visions, and he became a theologian. In 1758, he published The Earths in Our Solar System Which are called Planets and the Earths in the Starry Heaven, and Their Inhabitants; Also the Spirits and Angels There From Things Heard and Seen
, describing what he encountered as he he psychically traveled to the other planets.
In 1848, Margaret and Chase Fox of Hydesville NY near Newark NJ claimed that they could communicate with spirits -- spirits that communicated back by making cracking noises. This was the beginning of Spiritualism, and the Fox sisters were joined by numerous other spiritualist mediums. The movement continued despite the Fox sisters confessing in 1888 that they'd faked their spirit communications by cracking various joints, like toe joints.
Most spiritualists contacted ghosts of the dead, supernatural entities, but some of them contacted ET's, usually Martians. Hélène Smith
was one of them, and she even got some samples of a Martian language. Psychologist Théodore Flournoy examined those samples, and he found them to be a relex of French, her native language. A relexification, relex for short, is replacing the words in a language with other words, without changing its structure. Some people like to create and use constructed natural languages or conlangs, and such people often consider relexes of existing languages very amateurish and unimaginative.
In 1930, a psychic named Willard Magoon went on a psychic trip to Mars, where he discovered that that planet has lots of forests, parks, and gardens, and that its inhabitants had long used radios and electric cars.
I must note an early physical contact. Occultist Guy Ballard of the Theosophy-inspired I AM activity claimed in 1935 that he had a remarkable experience some years earlier in the Royal Teton mountains. In a cavern there, along with some other people, he watched as 12 Venusians, 7 male and 5 female, teleported in from their homeworld in a blaze of light. They then proceeded to play a concert with violins and harps, and they showed off on a reflecting screen a movie about technological achievements on their homeworld.