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?
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.