I hate to burst your bubble, but we don't have adequate documentary...to tell us when the decree to rebuild Jerusalem was issued.
Oh yes we do.
(Luk 20:17) And he beheld them, and said, What is this then that is written, The stone which the builders rejected, the same is become the head of the corner?
It is called, "The New Covenant". And it is Marvellous! Here is how we see to know when Jerusalem began to be rebuilt;
It started with "The Cornerstone"...
(Mat 21:42) Jesus saith unto them, Did ye never read in the scriptures, The stone which the builders rejected, the same is become the head of the corner: this is the Lord's doing, and it is marvellous in our eyes?
(Psa 118:22) The stone which the builders refused is become the head stone of the corner.
(Psa 118:23) This is the LORD'S doing; it is marvellous in our eyes.
(Isa 28:16) Therefore thus saith the Lord GOD, Behold, I lay in Zion for a foundation a stone, a tried stone, a precious corner stone, a sure foundation: he that believeth shall not make haste.
(Act 4:10) Be it known unto you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you whole.
(Act 4:11) This is the stone which was set at nought of you builders, which is become the head of the corner.
(1Pe 2:6) Wherefore also it is contained in the scripture, Behold, I lay in Sion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded... Unto you therefore which believe he is precious
Those who are blind to this and look for something "else" something "future" or something "physical" like the Pharisees did, are described further;
(1Pe 2:7)... but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner,
(1Pe 2:8) And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed.
This is how the goats are separated from the sheep.
If we recognize this "Building of God", we will know that it is "made without hands" (as opposed to a "physical" building "made with hands";
(Dan 2:45) Forasmuch as thou sawest that the stone was cut out of the mountain without hands...
(Mar 14:58) We heard him say, I will destroy this temple that is made with hands, and within three days I will build another made without hands.
(Act 7:48) Howbeit the most High dwelleth not in temples made with hands; as saith the prophet,
(Act 7:49) Heaven is my throne, and earth is my footstool: what house will ye build me? saith the Lord: or what is the place of my rest?
(2Co 5:1) ...we have a building of God, an house not made with hands, eternal in the heavens.
The following words of Paul should sober up those who think otherwise, as though some futuristic Jerusalem temple is unfulfilled words of the prophets. For that is a lie.
(1Co 3:9) ... ye are God's building.
(1Co 3:10) According to the grace of God which is given unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon.
(1Co 3:11) For other foundation can no man lay than that is laid, which is Jesus Christ.
(1Co 3:12) Now if any man build upon this foundation gold, silver, precious stones, wood, hay, stubble;
(1Co 3:13) Every man's work shall be made manifest: for the day shall declare it, because it shall be revealed by fire; and the fire shall try every man's work of what sort it is.
(1Co 3:14) If any man's work abide which he hath built thereupon, he shall receive a reward.
(1Co 3:15) If any man's work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.
(1Co 3:16) Know ye not that ye are the temple of God
, and that the Spirit of God dwelleth in you?