(This was originally going to be a comment, but I'm going to go ahead and make this an answer and explain why I'm not sure it is possible to effectively answer this question. I could well be convinced otherwise, though!)
Unlike obscenity, you don't know (old) iyashikei when you see it
So, here's the problem, as I see it. iyashikei is one of those things that is characterized less by the content of a work and more by the effect of that work upon its audience.
Today, content creators have a well-worn library of narrative approaches that they can use to make their work iyashikei (e.g. "cute girls doing cute things"), and so we can look at a present-day work and see how it uses these approaches to effectively "heal" the audience. Alternatively, we can look at how a work comports itself relative to "canonically" iyashikei works that it discourses with, like Aria and so forth.
But when we look at works that predate the iyashikei "canon" and its associated library of approaches, how do we effectively evaluate whether a work is or is not iyashikei? Based on how it makes you feel, I guess.1
But that doesn't help us come up with a good answer to "which was the first?". That's the issue - it's simply rather difficult to say what is or is not iyashikei the further into the past you go.
I strongly disagree with the reddit user's claim that Only Yesterday is iyashikei.
While it is, on the whole, a calm and relaxing movie, and happens to employ some of the narrative trappings common to modern iyashikei works (wistfulness for rural Japan, in particular), it pairs these elements with decidedly un-healing bits, like the various mishaps Taeko experiences during her childhood, and the obstacles she faces in her budding relationship with Toshio. It is a beautiful slice of Japanese life, but is it healing? No, at least not to me.
If we lifted Only Yesterday out of 1991 and released it for the first time in 2016, would we call it iyashikei? I don't think so. It is not, in my view, substantially in discourse with the modern "iyashikei canon".
Why is iyashikei a Thing, anyway?
There's something of an argument that the crystallization of iyashikei in the late 90s as a Thing (throughout Japanese media; not just in the otaku realm) is a direct response to the trouble Japan was experiencing at the time - the bubble had just burst, and Japan was really reeling for the first time since World War II. This explanation is pretty reductive, and it'd be silly to claim that the economy is the only (or even primary) cause, but it seems uncontroversial that Japan's national woes at the time did contribute to the reification of iyashikei.
Taken out of its context as a response to the Japanese zeitgeist of the 90s, does it even make sense to talk about iyashikei? I'm not sure that it does.
A long, rambling footnote
1 This is not to say that it is always impossible to identify a work as having a quality that was only effectively delinated after the work's creation.
Take, for example, the realm of gothic fiction. When Walpole wrote The Castle of Otranto, he wrote the first gothic novel, even though he could not have known that, since the idea of gothic fiction as a distinct thing did not come about until some years later. But we can nonetheless distinctly see that Otranto is a gothic novel (never mind the fact that the whole genre is named for Otranto to begin with), because there are specific narrative trappings that characterize gothic fiction (spooky castles, fantastic romances, etc.), and Otranto exhibits them.
But iyashikei works are not characterized by their narrative in this same way. Where, on the one hand, you have the (admittedly large) cluster of "cute girls doing cute things" anime, you also have "man has mystical encounters with spiritual entities" (Natsume Yuujinchou, Mushishi) and "parenting is great" (Usagi Drop, timeskip notwithstanding) and "shibe does shibe things" (Itoshi no Muco) and "whatever Glasslip is" (Glasslip), and I don't know how to identify a coherent commonality among all these things besides "they make me feel fuzzy inside".