As Giorgio Moroder eloquently says on Daft Punk's Random Access Memories, "why don't I use the synthesizer which is the sound of the future?" To put it plainly and most obviously, EDM would not exist without the synthesizer. It's feasible to say it could have without anything else on this list, but not the synthesizer.
Early synthesizers date back to the late 1890s, but it wasn't until 1965 when Robert Moog created his Moog synthesizer that the idea of a portable, self-contained instrument was introduced. The influence of the Moog spread throughout multiple genres, from classical to rock, with dance music producers being heavily influenced by the experimentations with the Moog that Moroder came up with. Everyone from Daft Punk to Four Tet have drawn some inspiration from the Moog, and the use of the synthesizer is widespread throughout the entirety of dance music.