Very early in 1e, I had a female illusionist (human, obviously, since that or gnome were your only options, then). She had some levels and then the DM/group wanted randomly decided to roll everyone's psionics (which we just didn't do, normally, bitd). She made the impossibly high cut!
What began as a bunch of random, sort of pointless, powers -she could levitate, which was kinda a huge deal without a spell at the time and was -for a bunch of comic book/fantasy/sci-fi/X-men nerds - obviously skinned as a limited telekinetic ability.
Eventually, over the years, into 2e, she was pulled out from time to time (and I would use her as an NPC when I dm'd) more and more retconned and reskinned that, while she had trained as an illusionist/had studied magic and knew about sorcery and spellcasting and such, her "illusionist spells" were all explained - and purposely chosen to be able to explain - as various psionic/psychic powers. Telepathy: visual illusions, mirror image, invisibility, phantasmal killer, dazing/knocking people out with "Color Spray," etc... Empathic powers: charm person, confusion, fear, et al. And minor telekinetic abilities: kept her levitation, "wall of fog" with ambient atmosphere/moisture, "shadow magic" became stuff that was semi-real psychic(what we'd now call "force")/telekinetic effects, etc... And thus, my first D&D "psychic" character was...well, not so much "born," as "evolved into."