The simplest way to prove Jerusalem fell in 587BC is using Ptolemys Canon. You can easily find it on the internet. Ptolemys Canon is merely a list of eclipses and astronomical observations, and the date they occurred, going back to around 750BC. The concept of "BC" didn’t exist back then so the date instead is made up of the name of the king and the number of years the king has been on the throne.
Because astronomers can calculate when eclipses should have occurred, even as far back as 750BC, astronomers have determined that Ptolomys Canon is completely accurate. Because Ptolemys Canon lists kings and when they came to the throne, we know that Nebuchadnezzar (who is specifically named in Ptolemys Canon) came to the throne in 605BC.
There is also now Archelogical evidence it was 587/586 as nmentioned in "The History of the Benjamin Region under Babylonian Rule" and "Jerusalem between Two Periods of Greatness: The Size and Status of the City in the Babylonian, Persian and Early Hellenistic Periods".
Also, why does the bible have to be correct on 70 years? Can't take that as fact when it has been proven Daniel was written around 160BC, and contains historical errors. The Jews don’t include Daniel as one of the prophets, but the book is included in the "Ketuvim" (ie the fiction section of the Hebrew Scriptures).
There is therefore plenty proof it is 587/586 but there is none for 607. The only proof used is the bible, which cannot be trusted.
More proof?
Jerusalem was under Babylonian siege for 2 years under the rule of King Nebuchadnezzar.
Jeremiah 52:4, 5* - "4 In the ninth year of Zed·e·kiʹah’s reign, in the tenth month, on the tenth day of the month, King Neb·u·chad·nezʹzar of Babylon came with all his army against Jerusalem. They camped against it and built a siege wall all around it. 5 And the city was under siege until the 11th year of King Zed·e·kiʹah."
The Bible states that Jerusalem was destroyed in the 19th year of King Nebuchadnezzar’s reign as king.
Jeremiah 52:12-14* - "12 In the fifth month, on the tenth day of the month, that is, in the 19th year of King Neb·u·chad·nezʹzar the king of Babylon, Neb·uʹzar·adʹan the chief of the guard, who was an attendant of the king of Babylon, came into Jerusalem. 13 He burned down the house of Jehovah, the king’s house, and all the houses of Jerusalem; he also burned down every large house. 14 And the walls surrounding Jerusalem were pulled down by the entire Chal·deʹan army that was with the chief of the guard."
Babylonians kept extremely detailed historical records of everything from receipts to the positions of the stars and large events in the nation’s history. By extracting data from the abundant number of cuneiform tablets created by the Babylonians, and using extremely accurate mathematical and digital models that track the movement of the planets and stars in the location where the records were written, it is possible to establish the date that King Nebuchadnezzar took the throne of Babylon, which was sometime between 605-606 B.C.E.
References:
James G. Macqueen, Babylon (1964)
The Cambridge Ancient History (12 vols., 1923-1939)
D. J. Wiseman, Chronicles of Chaldaean Kings (1956)
Thus, according to historical record as well as the Bible, it is indisputable that Nebuchadnezzar’s siege of Jerusalem began in his 17th year of ruling as King of Babylon, or 588-589 B.C.E. Two years later, the Babylonians breached the walls and destroyed Jerusalem and took some of the Jews captive. This happened in Nebuchadnezzar’s 19th year as king, or 586-587 B.C.E.
The Organization blatantly disregard archaeologically and historically verified fact and continue to state that Jerusalem was destroyed in 607 B.C.E., a full 1-2 years before Nebuchadnezzar was reigning as King of Babylon. Although prior to 605-606 B.C.E. Nebuchadnezzar was the commander of the Babylonian army, Jeremiah 52:4 states that Nebuchadnezzar was already King of Babylon and later at Jeremiah 52:12 states that Nebuchadnezzar had been ruling for 17-19 years by the time these events took place.