Yes the antichrist or false-christ will build it. And if you knew anything about prophecy you would know that Haggai was the prophet who lived when Zerubbabel and Joshua were building the 2nd temple not the 3rd. The 2nd temple exceeded the glory of Solomons temple because Christ himself showed up and hallowed it by his presence.
There is no prophecy that states that the Roman pope, who is the "man of lawlessness" and the "little horn" that destroyed the second temple, will build the third temple. You have fooled yourself into believing a lie that is not even found in the scriptures. You are also ignoring the prophecy in Haggai that states that the greater glory of the temple spoken there happens
after the nations are shaken, which we know happens at the seventh bowl of wrath in Revelation, where that greater temple is the temple Ezekiel saw in a vision, for it will be on on a very high mountain called Mount Zion, as he saw in his vision,
In visions of God he took me to the land of Israel and set me on a very high mountain, on whose south side were some buildings that looked like a city. He took me there, and I saw a man whose appearance was like bronze; he was standing in the gateway with a linen cord and a measuring rod in his hand. The man said to me, “Son of man, look carefully and listen closely and pay attention to everything I am going to show you, for that is why you have been brought here. Tell the people of Israel everything you see.”
I saw a wall completely surrounding the temple area. The length of the measuring rod in the man’s hand was six long cubits, each of which was a cubit and a handbreadth. He measured the wall; it was one measuring rod thick and one rod high. (Ezekiel 40:2-5 [NIV])
Which is the high mountain in Isaiah,
In the last days the mountain of the LORD’s temple will be established as the highest of the mountains; it will be exalted above the hills, and all nations will stream to it. Many peoples will come and say, “Come, let us go up to the mountain of the LORD, to the temple of the God of Jacob. He will teach us his ways, so that we may walk in his paths.”
The law will go out from Zion, the word of the LORD from Jerusalem. (Isaiah 2:2-3 [NIV])
Where we know this time happens AFTER the second coming of Jesus Christ, hence the reason people will say, "let us go up to the mountain of the LORD, to the temple of the God of Jacob. He will teach us his ways"
And also in Micah, where the temple will be built on a high mountain
In the last days the mountain of the LORD’s temple will be established as the highest of the mountains; it will be exalted above the hills, and peoples will stream to it. (Micah 4:1 [NIV])
And we even know that water flows from the temple Ezekiel saw, making the sea in Arabah fresh, which is the Dead Sea,
Then he brought me back to the door of the temple, and behold,
water was issuing from below the threshold of the temple toward the east (for the temple faced east). The water was flowing down from below the south end of the threshold of the temple, south of the altar. 2 Then he brought me out by way of the north gate and led me around on the outside to the outer gate that faces toward the east; and behold, the water was trickling out on the south side. 3 Going on eastward with a measuring line in his hand, the man measured a thousand cubits,[a] and then led me through the water, and it was ankle-deep. 4 Again he measured a thousand, and led me through the water, and it was knee-deep. Again he measured a thousand, and led me through the water, and it was waist-deep. 5 Again he measured a thousand, and it was a river that I could not pass through, for the water had risen. It was deep enough to swim in, a river that could not be passed through. 6 And he said to me, “Son of man, have you seen this?” Then he led me back to the bank of the river. 7
As I went back, I saw on the bank of the river very many trees on the one side and on the other. 8 And he said to me, “This water flows toward the eastern region and goes down into the Arabah, and enters the sea; when the water flows into the sea, the water will become fresh.[c] 9 And wherever the river goes,[d] every living creature that swarms will live, and there will be very many fish. For this water goes there, that the waters of the sea[e] may become fresh; so everything will live where the river goes. (Ezekiel 47:1-9 [ESV])
You are the one who does not know prophecy. Stop being stubborn and understand. You are in error and are not in the truth.