I doubt that it can be proved conclusively because we have to go outside of the Bible for secular dates. Secular dates are not something that I have any confidence in. I can only acquaint you with the work of Dr Floyd Nolen Jones which I reproduce below:
The Year Nebuchadnezzar Razed Jerusalem
Genesis
|
Event
|
Yrs.
|
AM
Age of Earth
|
Genesis
|
Event
|
Yrs.
|
AM Age of Earth
|
Ch. 1
|
Creation
|
0
|
0
|
7:6
|
The Flood when Noah was 600
|
|
1656
|
5:3
|
Seth born when Adam was
|
130
|
130
|
11:10
|
Arphaxad born when Shem was
|
100
|
1658
|
5:6
|
Enos born when Seth was
|
105
|
235
|
11:12
|
Salah born when Arphaxad was
|
35
|
1693
|
5:9
|
Cainan born when Enos was
|
90
|
325
|
11:14
|
Eber born when Salah was
|
30
|
1723
|
5:12
|
Mahalaleel born when Cainan was
|
70
|
395
|
11:16
|
Peleg born when Eber was
|
34
|
1757
|
5:15
|
Jared born when Mahalaleel was
|
65
|
460
|
11:18
|
Reu born when Peleg was
|
30
|
1787
|
5:18
|
Enoch born when Jared was
|
162
|
622
|
11:20
|
Serug born when Reu was
|
32
|
1819
|
5:21
|
Methuselah born when Enoch was
|
65
|
687
|
11:22
|
Nahor born when Serug was
|
30
|
1849
|
5:25
|
Lamech born when Methuselah was
|
187
|
874
|
11:24
|
Terah born when Nahor was
|
29
|
1878
|
5:28
|
Noah born when Lamech was
|
182
|
1056
|
11:26
|
Abraham born when Terah was
|
130
|
2008
|
11:10
|
Shem born when Noah was
|
502
|
1558
|
12:4
|
Abraham enters Canaan, age 75
|
75
|
2083
|
Scripture
|
Event
|
Yrs
|
AM Age of Earth
|
Gen. 12:4
|
Abraham enters Canaan and begins sojourn, age 75
|
75
|
2083
|
Gen 12:10; Ex 12:40; Gal 3:17
|
From when Abraham left Haran to enter Canaan until the Exodus from Egypt (to the very day)
|
430
|
2513
|
1 Kings 6:1
|
Exodus to start of Temple, 479 years (in the 480th year which is 479 years plus 16 days...)
|
479
|
2992
|
1 Kings 11:42; 6:1,37-38
|
Start of Temple to division of the Kingdom. Solomon reigned 40 yrs, Temple begun in his 4th year
|
37
|
3029
|
Ezek 4:4-6
|
Division of kingdom to destruction of Jerusalem in the 390th year (inclusively numbered = 389+)
|
389
|
3418
|
Without the use of any resources other than the Authorized Bible, the date Nebuchadnezzar burned Jerusalem and the Temple was...derived... by simply utilizing all the Scriptures exactly as recorded in the Chrono¬logical Compendium on page xiii. [Tables above] As already documented in our second chapter, these few passages established the year of the fall of the Kingdom of Judah in the 11th year of Zedekiah as AM 3418. The relevant Scriptures relating to the reigns of the kings of Judah were then charted in terms of AM years. This resulted in fixing the year of "the Captivity" as AM 3407.
Inclusively numbering 37 years from this first year of Jeconiah's (Jehoiachin) Captivity brought me to 3443 AM, the first year of the reign of Evil-merodach, son and successor of Nebuchadnezzar (2 Kings 25:27, cp. 2 Kings 24:12, 15). Counting back from 3443 AM, 3418 was found to be the 19th year of Nebuchadnezzar - the very year the Scriptures say he razed Jerusalem (Jer. 52:12-15). We have just seen in the above paragraph that this destruction took place in the 11th year of Zedekiah (2 Kings 25:1-7), thus confirming the synchronization of Judah and Babylon in 3418.
Numbering from Nebuchadnezzar's 19th year set AM 3399 as the year he ascended the throne. The Bible tallied that date with the 4th year of Jehoiakim (Jer. 25:1, cp. 46:2). The reader will note that connecting these two kingdoms was accomplished using only Scripture. No secular data whatsoever was consulted; neither was any needed.
With the kingdoms of Judah and Babylon thus firmly synchronized, all that remained was to convert the Anno Mundi years to BC. Of course, as "BC" is a secular designation, consulting such data will be necessary for this step.
The simplest, most accurate and most direct way to accomplish this is to begin with the year of Nebuchadnezzar's accession to the throne of Babylon. It is the most reliable point of contact between the secular kingdoms and that of the Hebrew for the chronologer to so convert. As stated earlier in this treatise, Nebuchadnezzar's accession year is fixed by the well-documented lunar eclipse recorded by Ptolemy. This eclipse took place during the fifth year of Nebuchad¬nezzar's father, Nabopolassar. Again, it has been dated as 22 April, -620 (Julian Period, the historical Gregorian date is April 15, 621 BC).
The Canon of Ptolemy and the Babylonian Chronicles tell us that Nabopolassar, reigned twenty-one years. Hence, if we take 621 BC as the fifth year of his reign, the year of his death and the accession of his son will be fixed at 605 BC. Again, Jeremiah 25:1 states that Nebu¬chadnezzar's first year was the fourth year of the reign of Jehoiakim and this determines the BC date for that Judaic sovereign. Jeremiah also records that the Temple was burned in the nineteenth year of Nebuchadnezzar (Jeremiah 52:12-14, also 2 Kings 25:8); thus, the date for that conflagration is established as 586 BC.
Extract from Page 309:
The Chronology of the Old Testament Dr. Floyd Nolen Jones 16th Edition.
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I hope you have found this helpful.
God bless you,
Glenn