Jews also reached as far east as India.  There is a very old community there, many of whom claim to be descended from Jews who fled the Romans at the time of the destruction of Jerusalem in 70 AD.  This community was one of the trade connections for caravans coming from Europe to trade for spices, etc.

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It is my understanding that the assyrians took most of the lost tribes of Israel to Kashmir, where DNA has proved a link of the current natives with Isreal. It is my belief that this is where Jesus returned after his failed crucifixion, so he could continue his ministry to the tribes of Israel. He was also there as a child, during that time he was known as Issa.
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I don't know about Jesus, but I do know that although SOME Jews were carried off into slavery by the Assyrians and the Babylonians, it was not ALL the Jews.  The farmers & peasants were left behind to work the land for the conquerors.  The Samaritans were descendants of Jews who were NOT taken captive into exile.  That is why their descendants today do not accept the writings of the biblical Prophets, which were written during the Babylonian Captivity.

Also relevant to the Jesus issue is that when Jesus & Mary fled into Egypt, there was already a HUGE Jewish community in Alexandria.  So he was not going to study with the Pharoahs, he was probably educated by fellow Jews, where he may have learned Jewish mysticism concepts and techniques in existence in that community.