I think the question may be confusing two of the 70 year prophecies.
There is a prophecy that 70 years were allocated to Babylon, after which it would be punished for invading. That was 609 BC - 539 BC when the Achaemenids took over.
In 538, Cyrus issues a decree that captive populations can return, and so Daniel starts investigating what the scriptures say about the desolation:
Jeremiah 29:10 (KJV 1900)
10 For thus saith the LORD, That after seventy years be accomplished
at Babylon I will visit you, and perform my good word toward you, in
causing you to return to this place.
But the desolation does not come to an end with Cyrus issuing a decree -- there were three proclamations of the same decree, by Cyrus, by Darius the Great, and by Artaxerxes.
It was the decree of Darius, who not only reiterated the decree of Cyrus but also collected some of the gold and treasures that were taken from the Temple and returned them, that triggered the end of the desolation. When did it happen?
Haggai 2:18–19 (KJV 1900)
Consider now from this day and upward,
From the four and twentieth day of the ninth month,
Even from the day that the foundation of the LORD’s temple was laid, consider it.
Is the seed yet in the barn?
Yea, as yet the vine, and the fig tree,
and the pomegranate, and the olive tree,
hath not brought forth:
From this day will I bless you.
Haggai issued this prophecy "In the four and twentieth day of the ninth month, in the second year of Darius" (Haggai 2.10). Darius came to power in 522 BC so that would be the ninth month of 520 BC. This is when the desolation ends and the blessings begin.
This would point to 589 BC as the start of the desolation (as inclusive counting was used, in which a portion of a year counted as a whole year, and the desolation lasted into the ninth month of 520). This is the start of the last siege of Jerusalem by Babylon. The walls of Jerusalem were breached in the fourth month of 587 BC, about a year and a half after the siege began.
2 Kings 25:8–9 (KJV 1900)
8 And in the fifth month, on the seventh day of the month, which is
the nineteenth year of king Nebuchadnezzar king of Babylon, came
Nebuzar-adan, captain of the guard, a servant of the king of Babylon,
unto Jerusalem: 9 And he burnt the house of the LORD, and the king’s
house, and all the houses of Jerusalem, and every great man’s house
burnt he with fire.