Daniel 1:1,2 - In the third year

1:1

The events are dated as starting from the “third year of the reign of Jehoiakim king of Judah”. Now Babylon and Judah had different systems of counting dates. Under the Babylonian system this would have been 605 BC, since the first full year of his reign was New Year’s Day after his succession in 608 BC. Under the system used in Judah the year of accession was counted as the first year, so under that system this would have been his fourth year. Things like this can account for a number of apparent discrepancies in Bible dates. E.g. Jer 25:1 refers to this as the fourth year. Since Daniel was writing in Babylon it would be natural for him to use the Babylonian system.

1:2

As we have been reading in Jeremiah and Ezekiel, Judah, along with many temple artefacts, were taken off to Babylon. This happened as a result of God’s judgement upon Judah’s sin. There were three main deportations, one in 605 BC (the one including Daniel and his friends), 597 BC which included Ezekiel, and a third after the destruction of Jerusalem and the temple in 586 BC. Note that it says “the Lord delivered ...”. All the events were in God’s hands. Note that this verse does not necessarily imply that Jehoiakim went to Babylon, 2 Kings 24:6 says he died in Judah.