Daniel 1:3 (ESV)

3 Then the king commanded Ashpenaz, his chief eunuch, to bring some of the people of Israel, both of the royal family and of the nobility,

Nebuchadnezzar does not just take items from the temple to Babylon in 605 BC. He also orders that some of the children of the prominent people of Judah are brought to Babylon. These do not include boys from the tribe of Judah only; they are also from the other tribes. The fact is that the ten tribes are already in exile at this time, but a small portion of them have stayed behind. Some of them have also gone to live in Judah (see 2 Chronicles 30:1f, 2 Chronicles 34:9). Sons of the family of David and boys of other prominent families among God’s people are sent to Babylon.

Ashpenaz, who is one of the more important people at Nebuchadnezzar’s court, is to take care of them. Ashpenaz also receives instructions concerning the kind of boys they should be. Not every son of a distinguished native of Judah qualifies.