The short answer is DC, but it's a complex question.
Golden Age comics all had their own siloed enviroments, and it wasn't until the 1940 All Star Comics #3 introduced the Justice Society that they even shared a universe. All Star would later merge with two other publishers to form DC.
Wonder Woman was the first character to visit an parallel Earth in 1953, where different versions of everyone lived alternate lives.
DC rebooted all of their characters, starting the Silver Age of comics. In 1961, Silver Age Flash Barry Allen crossed over to the Golden Age world, meeting Jay Garrick. This is considered the true beginning of the DC Multiverse as a plot point. The Wonder Woman parallel world would occasionally pop up, but wasn't a major part of the continuity the way Flash of Two Worlds was.
Marvel introduced their own Multiverse in the 1970s in the Captain Britain series, and the idea became the basis for the popular What If...? series.
DC also introduced the Multiverse in their Arrowverse/Supergirl crossover event, establishing that all of the TV shows and movies could theoretically cross over, but the DC shows were far better received than the films.