No, you cannot know the date of the Rapture.

If you notice, all or almost all prophecy teachers are relying heavily on signs, on Israel's feast days, or both. They seem to have missed these verses

Isaiah 1:13-15
"Bring no more vain oblations; incense is an abomination unto Me; the new moons and sabbaths, the calling of assemblies, I cannot away with; it is iniquity, even the solemn meeting. Your new moons and your appointed feasts My soul hateth: they are a trouble unto Me; I am weary to bear them. And when ye spread forth your hands, I will hide Mine eyes from you: yea, when ye make many prayers, I will not hear: your hands are full of blood."

And as for signs, we get this

Matthew 12:39
"But He answered and said unto them, An evil and adulterous generation seeketh after a sign; and there shall no sign be given to it, but the sign of the prophet Jonas."

Now a question: how did God inform Isreal about the time of Messiah's first advent? The answer is, Daniel 9:25. And it was straightforward and accurate to the day. No signs, no feast day, just "this is the date, expect Him," 69 weeks of years or exactly 173,880 days from the decree of king Artaxerxes (who was a helf Jew, by the way, the son of Ruth and Ahasuerus, the Hebrew name of king Xerxes) on March 14, 445BC (the decree mentioned in Dan 9:25), terminating at April 6, 32AD, the date of the Triumphal Entry. But they missed it. Which is why Jesus held them accountable for not knowing the time of their visitation in Luke 19:41-44.

[reasonsforhopejesus.com]

Now if prophecy is as much pattern as it is prediction and fulfillment, it would be more likely than not that God would also give a date of an event in relation to the 2nd Advent outright in another cryptic passage. Again, out from the Torah, the word of God to the Jews. And again addressed to Israel.

Hosea 6:1-2
"Come, and let us return unto the LORD: for He hath torn, and He will heal us; He hath smitten, and He will bind us up. After two days will He revive us: in the third day He will raise us up, and we shall live in His sight."

Clearly this talks of a reconciliation between Messiah and Israel, which would be sometime after the Second Coming. And it will be two "days" or 2000 Jewish years (or 720,000 days) after the smiting. I'm not being dogmatic about this, but I believe that here you have the date given of the reconciliation of Israel to Messiah (Zech 12:10, arguably, the start of the Millennial Reign) from the terminus a quo of the "smiting" on Aug 6, 70AD, the day the 2nd temple came crashing down. But you'll have to do the Math. You won't read about this anywhere else because I did not copy this from anybody. Its just a discovery brought about by observation and many years of studying prophecy.

On a side note, the greatest medieval Jewish rabbinic sage by the name of Maimonides (aka Rambam) finally figured out Daniel 9:25 some 1,300 years too late. But his conclusion? God changed His mind and did not send the Messiah What made him think that way? The Talmud, which has become the lens by which the Jews read scripture, and the leaven Jesus warned Jewish believers about. But what gets me all excited about Rambam? That by simply studying the creation account, he came to the conclusion that there are 10 dimensions in creation. This in the 1300's, long before scientists even started to think about them.

[en.m.wikipedia.org]