Here's the description of the destruction of the temple and the city according to Josephus:
[Titus] Caesar gave orders that they should now demolish the entire city and Temple, but should leave as many of the towers standing as they were of the greatest eminence; that is, Phasaelus, and Hippicus, and Mariamne; and so much of the wall enclosed the city on the west side. This wall was spared, in order to afford a camp for such as were to lie in garrison [in the Upper City], as were the towers [the three forts] also spared, in order to demonstrate to posterity what kind of city it was, and how well fortified, which the Roman valor had subdued; but for all the rest of the wall [surrounding Jerusalem], it was so thoroughly laid even with the ground by those that dug it up to the foundation, that there was left nothing to make those that came thither believe it [Jerusalem] had ever been inhabited. This was the end which Jerusalem came to by the madness of those that were for innovations; a city otherwise of great magnificence, and of mighty fame among all mankind. (My underline)
The city was leveled. That is desolation.
Abomination of desolation standing in the holy place refers to an intact Temple, complete with a holy place.
“Therefore when you see the abomination of desolation,’ spoken of by Daniel the prophet, standing in the holy place” (whoever reads, let him understand), Matthew 24:15
It is in Daniel that we find understanding.
The city and sanctuary were destroyed in 70 AD, which is found in verse 26.
“And after the sixty-two weeks
Messiah shall be cut off, but not for Himself;
And the people of the prince who is to come
Shall destroy the city and the sanctuary.
The end of it shall be with a flood,
And till the end of the war desolations are determined. Daniel 9:26
The Romans destroyed the city and temple in 70 AD.
The Abomination of Desolation doesn’t occur until verse 27 and has Temple activities involved, which indicates a restored Temple with sacrifices.
Then he shall confirm a covenant with many for one week;
But in the middle of the week
He shall bring an end to sacrifice and offering.
And on the
wing of abominations shall be one who makes desolate,
Even until the consummation, which is determined,
Is poured out on the desolate.
Daniel 9:27
It is the prince who is to come that will confirm a covenant with many for one week.
This refers to the 70th week.
During that time the temple will be rebuilt.
This is what Jesus was referring to in the Olivet Discourse.
JLB