It is hypothesis that White Supremacy began in 323 BC with Alexander the Great conquering parts of Asia and Africa. Was Greece the 1st White empire?

Alexander was not the start of White Supremacy, or as I prefer to call it; White Domination.

Alexander, even though he controlled a wide range of territory was still regional despot governing a regional (not global) empire.  Like you said, he only held parts of Asia and Africa. There were other rival empires, nations, and states across the globe. I would call the Greeks the first successful White imperialist however; to rule over non-White peoples and territories.

The Greeks are the founders of Western Culture (which the patch together from interactions with African and Asian civilizations that predated Western Civilizations). Greeks also gave the world the foundation of the concept of “White” people, or Whiteness, but they had not refined it.  

The British, in the 1600s should be credited with laying the foundations for White Domination, or Global White Domination; they did more than invade and conquer territory, they engaged in creating a global Western monoculture, imposing a universal economic and political systems.

White Domination is a very new concept and condition for the world, and it will be one of the shortest lived systems the world has ever know, provided that the world is not totally stripped of complex life forms by this Omnicidal System of White Domination.