I would like to know who the first people to come up with the idea of reed instruments of any kind
Well, people in the outdoors with leisure time. Now outdoor jobs in prehistoric times were not all that unusual, but leisure time may have been. Hunters might have started reed instruments from primitive bird calls. Shepherds are obvious candidates for perfecting those in leisure time, and are also associated with ancient flutes. Shawms are medieval instruments but have antique predecessors: Egypt with its papyrus-grounded culture would be an obvious candidate for pre-antique versions of reed instruments.
This is more of an archaeology question than a music question, but it is generally agreed upon by the scientific community that the oldest known instruments are paleolithic-era bone flutes dating back to at least 42,000 years ago. As flutes are a type of reed instrument, this should answer your question!