Because the Southern Kingdom wasn't taken into exile in Babylon until after the Northern Kingdom of Israel were captured by the Assyrians, I chose to use Judah's kings as time markers.

After Solomon's Temple, the next breadcrumbs to follow in the Bible are the life of Solomon's son, Rehoboam who took his place ruling over the southern kingdom of Judah. Since 1 Kings 11:42-43 says Solomon ruled for 40 yrs., and he started the construction of the Temple 4 yrs. into his reign, we can conclude Rehoboam became king about 36 yrs. after the Temple completion. When we continue to 1 Kings 14, we read that Rehoboam was 41 when he became king and that his tenure lasted 17 yrs. If it was less than a yr. from the time Solomon died to when Rehoboam became king, then 53 yrs. passed from the Temple completion to the death of Rehoboam.

Event, people Duration
(yrs.)
Passages
Rehoboam, king of Judah 53 1 Kings 11:42-43, 1 Kings 14
Abijah, king of Judah 3 1 Kings 14:31, 1 Kings 15:1-8
Asa, king of Judah 41 1 Kings 15:9-10, 2 Chronicles 16:13
Jehoshaphat, king of Judah 25 1 Kings 22:42, 2 Chronicles 20:31
Jehoram (Joram), king of Judah 8 2 Kings 8:16-17, 2 Chronicles 21:1-5
Ahaziah, king of Judah 1 2 Kings 8:24-26, 2 Chronicles 22:2
"Queen" Athaliah (usurper) 6 2 Kings 11, 2 Chronicles 24
Joash, king of Judah 40 2 Kings 12:1, 2 Chronicles 24:1
Amaziah, king of Judah 29 2 Kings 14:1-2, 2 Chronicles 25:1
Uzziah (Azariah), king of Judah 52 2 Kings 15:2, 2 Chronicles 26:1-3
Jotham, king of Judah 16 2 Kings 15:32-33, 2 Chronicles 27:1
Ahaz (Jehoahaz), king of Judah 16 2 Kings 16:1-2, 2 Chronicles 28:1
Hezekiah, king of Judah 29 2 Kings 18:2, 2 Chronicles 28:1
Manasseh, king of Judah 55 2 Kings 21:1, 2 Chronicles 33:1
Amon, king of Judah 2 2 Kings 21:19, 2 Chronicles 33:21
Josiah, king of Judah 31 2 Kings 21-22, 2 Chronicles 34:1
Jehoiakim, king of Judah 11 2 Kings 23:34-36, 2 Chronicles 36:5
length of the Babylonian exile 70 Jeremiah 29:10
Total duration: 488  

Jeremiah 29:10 (70 yrs. of Babylonian captivity)
10. This is what the LORD says: "When seventy years are completed for Babylon, I will come to you and fulfill my gracious promise to bring you back to this place.

53 + 3 + 41 + 25 + 8 + 1 + 6 + 40 + 29 + 52 + 16 + 16 + 29 + 55 + 2 + 31 + 11 + 70 = 488 yrs. from the completion of king Solomon's temple to the end of the Babylonian exile.

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