When did the word “Einstein” begin to be used popularly as slang to refer to “genius”, both sincerely and sarcastically?
I’d guess sometime not long after 1905.
My guess is that Einstein’s name came to be used in the sense described by OP in the 1920s.
He was unknown to the public until 1920.
That year results of observations made during the solar eclipse of 5/29/19 were published,
confirming that starlight was deflected by the Sun by an amount predicted by General Relativity.
Einstein then became an overnight sensation, and remained one for the rest of his life.
[tangential hijack]
On Saturday morning cartoon kidvid (early 1960’s or so?), I saw cartoonish images of Einstein being used every now and then, representing some sort of generic genius/professor. I had no idea until years later that this was a real person.
[/tangential hijack]
Trying to search newspapers and books for the slang use is pretty difficult.
Looks like early 40’s is the beginning.
Einstein took a vacation in California in 1931 and hobnobbed with the Hollywood elite. Charlie Chaplin brought him to the premiere of City Lights, e.g. All this was covered extensively by the newspapers and I think also the newsreels. That may have taken him from a figure in newspaper headlines to an embodiment of a scientist.
You can read more about Einstein’s adventures in Hollywood here, as long as you realize that it’s all fiction.