My accordion and pump organ are part of the great family of free reed instruments.
Free reed pump organs were first developed in Europe in the late 1700s/early 1800s. Piano accordions arose in Europe in the mid-1800s, preceded by button accordions, harmonicas, and pump organs, but the concept goes back thousands of years to East Asian mouth organs including the Chinese sheng. The development of the keyboard itself is much older, with the earliest known precursor, the hydraulis pipe organ, dating to the 3rd century B.C.E.
For more info:
- Western Free Reed Instruments by P. Missin, with a lot of great related links
- keyboard history from Encyclopaedia Britannica