Talmud Yerushalmi, Yoma 1a, the Rambam, King David, The Vilna Gaon on The Temple Mount

In respectful response to feedback to this post I have added a Caveat and a Postscript

"I heard from my teacher and father-in-law, who was the chief disciple of Rebbe Yechiel Michal of Zlotchov, that once when the Baal Shem Tov was traveling on the road, he stepped into a wooded area to pray the afternoon prayer. His disciples were dumbfounded to see him hitting his head against a tree, crying and screaming. Afterward, they asked him what had happened. He explained that he had seen, with divine inspiration, that in the generations before the coming of the Moshiach there would be a multitude of rabbis, and that they would be the very ones who would impede the redemption." [Otzar Chayim]

The Sages taught, "Any generation in which the Temple is not built,

 it is as if it had been destroyed in their times" (Yerushalmi, Yoma 1a)

"If I am not for myself who is for me? And being for my own self, what am 'I'? 

And if not now, when?" (Hillel the Elder)

Caveat 
While I present valuable information concerning our Temple Mount
The Rabbonim have cautioned Jews not to go up
(see postscript at bottom), 

while their opinion is based on Halacha

there are alternate viewpoints

WHEN WILL IT EVER BE THE RIGHT TIME? 

WHAT WE KNOW and DO NOT KNOW.

(T)he idea of actually going up to the Mount under very specific conditions is not unfounded. Rambam (Beit HaBachira 7:1-7) enumerates several ways in which one is required to show fear and awe for the Temple: One may not enter with his staff, shoes on his feet, his money belt, dust on his feet, nor spit. He may not use the Mount as a short cut and may not go on the Mount except for a mitzvah. One who has finished his service may not leave with his back facing the Temple, rather he must walk backward toe to heel. He concludes by saying, "Even nowadays that the Temple has been destroyed, one is obligated to act as when it was built: He may not enter except in a place where it's permitted to go, he may not sit in the area of the Azara, and may not act frivolously opposite the eastern gate facing the Holy of Holies."

Rambam (Beit HaBachira 7:1-7

The least stringent area is called Har HaBayit, [the third area] which is the open area outside the Temple complex.

(R)egarding the impurity resulting from contact or exposure to a dead body (2), even though entering the Azara and Ezrat Nashim is also severe (3), entering the rest of the Mount (the third area) is permitted

Beit HaBachira 7:15, Biat Mikdash 3:4

(T)he Mishna (Kelim 1:8) explicitly states that a Tameh Met is allowed on the Mount. (...) the Bartenura comments that even a dead body itself is allowed to be brought onto the Mount. Tosefot Yom Tov explains that the source of the Bartenura is from the Tosefta on the verse, "and Moshe took the bones of Joseph with him," which explains the verse to mean "with him into the camp of the Levites", corresponding to the Har HaBayit

Mishna, Kelim 1:8, see also Tiferet Israel who cites Pesachim 67

(T)he more stringent forms of impurity pose less of a problem than the less severe Tumat Met. In order to go onto the Mount at all, both men (4) and women (5) would have to be pure from seminal discharge, and in addition women would have to be pure from menstrual impurity (this would generally exclude unmarried women who do not immerse, 6). Even then, the remaining impurity from contact with the dead would prevent one from entering anywhere other than the outermost area described above as Har HaBayit.

A point for further study is the idea that for the purpose of building the Temple, one might be able to enter all areas of the Mount, even with Tumat Met, and even in the Holy of Holies. Rambam writes (Beit HaBachira 1:1) that it is a positive Torah commandment to build a house for Hashem that is fitting to offer in it sacrifices.

Rambam, Beit HaBachira 1:1

(I)n keeping with the words of the Vilna Gaon (in Aderet Eliyahu) that initially

we must desire to build the Temple of our own initiative

afterwards G-d will answer our request

Aderet Eliyahu

Malbim echoes this sentiment when he writes, "We find that David sought to build the Temple himself and didnt wait for a prophet to come to tell him. David learned this from the verse, You shall inquire after His dwelling and come there (Deut. 12:5). Inquiring means probing into the matter oneself until one brings it to fruition. This is the meaning of Sifri 8 'Inquire and find'. It teaches that G-d will not reveal the Temple's location through a prophet until the Jewish people make an effort to inquire and search for it. Only then will he send a prophetic spirit from above to reveal it.”

Malbim, Devarim 12:5

Ohr Somayach Institutions

Also of further interest:

The Vilna Gaon on Chumash Devarim

Historical Background On the Struggle For Jewish Prayer On The Temple Mount: Translated Excerpts from Rabbi Shlomo Goren's book on Har Habayit [also called Meishiv Milchama Volume 4]

Issues Involving The Ascent To The Temple Mount - An Exchange Of Letters Between S. Scheinman and Rabbi Avigdor Neventzal

Location of the Temple. Temple Mount Movies

The Third Temple Vilna Gaon

POSTSCRIPT:  Due to the nature of the above information and the political situation, the Israeli Government has taken a very apprehensive position vis-a-vis the nations,
and in support of the call of the Rabbonim