Blitzkrieg was a propaganda term; the actual doctrine was Bewegungskrieg - Maneuver Warfare. And it's at least as old as the 1820s, when the Prussian General Staff began to analyze their defeats in the Napoleonic Wars. It was on the Eastern Front of WW1 however where they saw the potential for mechanized maneuvering and deep-penetration as a viable operational and strategic element, and they understood that cutting off an enemy is worth disrupting your own clean "lines" in the process, and that is what led to the Wehrmacht's stunning victories in France in 1940, and the initial success of Barbarossa in 1941.
On the western front, with the trenches being so long and so close together in places, and the ground so muddy, you couldn't use cavalry or trucks for those swift operations that would carry you to Paris, and the tank and airplane (at least as a bomber) were still in embryonic form... it took much of the Bewegung out of the Krieg pretty quickly.
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