To really understand the origins of MIDI, you need to go all the way back to before there were digitally controlled synthesizers and computers, In fact you need to go back before there was even electricity to the very first mechanical music machines.
The very first mechanical musical instruments were documented in the Book of Ingenious Devices published in 850 AD by three Iranian brothers known collectively as Banu Musa. They describe 100 mechanical devices including two automated musical instruments- a hydro powered organ that played music based on interchangeable cylinders that had music patterns on them.
This cylinder with raised pins on the surface remained the basic device to produce and reproduce music mechanically until the second half of the nineteenth century.”
Charles B. Fowler (Music Educators Journal © 1967),
The first computer?
The Banu Musa also invented an automatic flute player that actually may have been the first programmable machine or computer. The flute sounds were produced by steam and you could modify settings to create different sounds and patterns. It almost sounds like what MIDI does today! These automated music machines were used for entertainment at parties just as today we stream music from our smartphones.
Mechanical Music Box
The same basic system of cylinders with music patterns was used for centuries and is still used today in carillons and music boxes.
https://www.midi.org/articles/midi-and-player-pianos
The golden age of mechanical music machines really came in the late 19th century and early 20th century with player pianos and orchestrions.