Afaik, nobody knows where/when the myth started because it started organically, rather than being something like bumblebees not being aerodynamically sound, where there was poorly explained information that got spread from that point.

The most popular theory of the origin is that since veins look blue, and thus were drawn as such in anatomy illustrations, the idea got spread through wide ranging multi point origins. I’ve seen people argue for the veins looking blue as the genesis, with the idea being that someone asked why blue veins ran red when cut. But I’ve seen it argued that it wasn’t until the illustrations came along and faulty information was needed to explain that that it spread far enough to actually be taught by people that should have known better (like some folks, I ran into the idea in jr high, knew it was wrong because of family with medical training, and got in trouble for trying to say so).

But I have looked a few times over the years to see if I could run down a definitive origin story, and never have. Mind you, me looking involved searching for articles about it, rather than trying to run down historical references direct because I don’t have that kind of access.