[Stanwood_Dave]

Your close ref: time frame.

Alex I'll take repeating firearms for a $1000.00.

What was the first ever called "Machine Gun?"

What is known as the "Puckle Gun," a.k.a. (also known as the defense gun) was a primitive crew-served, manually-operated flintlock revolver patented in 1718 by James Puckle, (1667–1724) a British inventor, lawyer and writer. It was one of the earliest weapons to be referred to as a "machine gun", being called such in a 1722 shipping manifest.

Hint: check out the "AIR-RIFLE" issued by the 3rd POTUS {March 04, 1801 - March 04, 1809} Jefferson to Lewis & Clark.

[Stanwood_Dave]

Girandom Air Rifle {Not a Musket, but a rifle.} {Known as the "Wind Rifle" in Austria 1780's.} Could shoot 20 rounds in less than 30 seconds. Also used during the Napoleonic war's. POTUS Jefferson (the third POTUS from 1801 to 1809,) outfitted {led by Capt. Meriwether} Lewis & {Lieut. William} Clark Expedition with this gun, to explore the Louisiana Purchase and the Pacific Northwest.

Other multi-shot weapons:

"Hand Cannon(s)" from the 14 century.
"Hand Cannon(s)" that could shoot up to 10 rounds.
"Volley Gun(s)" some having up to 20 barrels. 16 century stuff.
Duck Foot Pistol.
Pepperbox Revolver. hundreds of years before the 2nd Amendment.
Belton Flintlock (Was offered for sale to the U.S. congress of 1776)