You can't know that.
Anthropologically Caucasians include all or part of the populations of Europe, North Africa, the Horn of Africa, and West, Central and South Asia. There are Indians who qualify.
In the US census "white" includes "a person having origins in any of Europe, the Middle East or North Africa." Brazil has a similar definition. These are the largest nations who define "white."
Jesus, a Galilean, came from the Middle East and could very well have been a Caucasian / "white."
If you're classifying white as Caucasian, then he was Caucasian. But almost surely not white, nor blue eyed. Practically all arabs are Caucasian including Sadaam Hussein. Hispanics are Caucasian and by that criterion, therefore white. Hence the white/non-Hispanic white/Hispanic option of government forms.
Cleopatra was white as well, Persian to be specific, as was the Ramses line of Pharohs. Redheads. Nubian Pharos were Negroid, and very black. Egyptian culture was not a color based racist society. If you lived Egyptian culture, you were Egyptian.
American racism is it's own animal, created for a purpose, and perpetuated by racist Americans, though the slave trade is over, now we trade in human women and children mostly. No need to create a criteria to justify discrimination against them, just kidnap them and sell them.