This article from the blog at DCComics.com identifies the story in Wonder Woman #100 (AUG58) as the first multiverse story: "The Forest of Giants!/The Challenge of Dimension X" (16 pages) featuring an identical twin of Wonder Woman.
Just after that, 10-year-old me picked up two consecutive issues of Adventure Comics off the spinner rack. Adventure Comics #252(SEP58) and #253(Oct58) had the first and second parts of a continued Green Arrow story (12 pages in all) illustrated by Jack Kirby. Enormous arrows are investigated by Green Arrow and Speedy. It turns out that they were shot through a comet-caused (those pesky comets) dimensional gateway by the child (!) of a giant alien counterpart of our Green Arrow (dressed exactly like him).
Were there any multiverse stories before 1958. In DC comics? In other comics?
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It turns out that the DC article is incorrect. An earlier issue of Wonder Woman establishes the multiverse concept. This is a story that is canon.
The Hollywood Reporter actually came up with the issue number, but only had a paragraph and no illustrations.:
Wonder Woman #59 (MAY-JUN53).
When I googled it I found this article from Comic Book Resources which provides great detail.