Your quote from Matthew's 24th chapter is an accurate one in stating that no one will know the "exact" time. There are two, portions of Scripture in Chapter 24 that relate to that "end times" situation.
The first is: Matthew 24:32-33 (NIV2011)
32 “Now learn this lesson from the fig tree: As soon as its twigs get tender and its leaves come out, you know that summer is near.
33 Even so, when you see all these things, you know that it is near, right at the door.
I believe, the reference in the above verse relates to "Day of the Lord", the "Coming of God's Wrath" upon mankind and the Earth and those who, like myself, believe in a "Pre-Wrath" rapture believe that when Christ does return that as Paul taught in 1Thessalonians 4th and 5th Chapters & 2 Thessalonians 2nd Chapter, that Christ will bring, to meet Him in the Sky, the spirits/souls of those who have died first then those spirits/souls of those currently alive at the time of His coming. AFTER that God's Wrath will be released upon the Earth and mankind as mentioned and recorded in Revelation 8-19 Chapters
The second being: Matthew 24:36-39 (NIV2011)
36 “But about that day or hour no one knows, not even the angels in heaven, nor the Son, but only the Father.
37 As it was in the days of Noah, so it will be at the coming of the Son of Man.
38 For in the days before the flood, people were eating and drinking, marrying and giving in marriage, up to the day Noah entered the ark;
39 and they knew nothing about what would happen until the flood came and took them all away. That is how it will be at the coming of the Son of Man.
The above section indicating that for those, not looking for Christ return, and looking at the signs of those day that the Day of the Lord (God's Judgment upon mankind and the Earth) will come upon them as a thief in the night and as the flood came upon the people of Noah's day who were just carrying on as if nothing would happen, so it will be in the end days. People will be ignorant to the signs and to God's Word and warnings up and until they are caught up in it.
Consider also: 1 Thessalonians 5:1-11 (NIV2011)
1 Now, brothers and sisters, about times and dates we do not need to write to you, 2 for you know very well that the day of the Lord will come like a thief in the night. 3 While people are saying, “Peace and safety,” destruction will come on them suddenly, as labor pains on a pregnant woman, and they will not escape.
4 But you, brothers and sisters, are not in darkness so that this day should surprise you like a thief. 5 You are all children of the light and children of the day. We do not belong to the night or to the darkness. 6 So then, let us not be like others, who are asleep, but let us be awake and sober. 7 For those who sleep, sleep at night, and those who get drunk, get drunk at night. 8 But since we belong to the day, let us be sober, putting on faith and love as a breastplate, and the hope of salvation as a helmet. 9 For God did not appoint us to suffer wrath but to receive salvation through our Lord Jesus Christ. 10 He died for us so that, whether we are awake or asleep, we may live together with him. 11 Therefore encourage one another and build each other up, just as in fact you are doing.
Above, written by Paul unto the Thessalonian Church, he reminds them, as he addresses them as "brothers and sisters" that they know about the "day of the Lord" (day of God's coming Judgment) coming for they (brothers & sisters) are not in darkness (verse 4). So it is the unsaved, those who are not looking that will be caught unaware as a thief in the night.
The above doesn't by any means settle debates or the argument but creates many questions in and of itself. Consider the rapture. Many do not believe in a rapture at all and many do. For those that do another question can be ask or considered.
For those that do believe in a Rapture, as I do, and considering Paul's description of the rapture, specifically the following: 1 Corinthians 15:51-54 (NIV2011)
51 Listen, I tell you a mystery: We will not all sleep, but we will all be changed— 52 in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed. 53 For the perishable must clothe itself with the imperishable, and the mortal with immortality. 54 When the perishable has been clothed with the imperishable, and the mortal with immortality, then the saying that is written will come true: “Death has been swallowed up in victory.”
(sleep being death) and (compare vs 52, above, to Matthew 24:30-31)
1 Thessalonians 4:13-18 (NIV2011)
13 Brothers and sisters, we do not want you to be uninformed about those who sleep in death, so that you do not grieve like the rest of mankind, who have no hope. 14 For we believe that Jesus died and rose again, and so we believe that God will bring with Jesus those who have fallen asleep in him. 15 According to the Lord’s word, we tell you that we who are still alive, who are left until the coming of the Lord, will certainly not precede those who have fallen asleep. 16 For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. 17 After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever. 18 Therefore encourage one another with these words.
In the above verses, which mirror Matthew 24:30-31, indicate that the souls/spirits of the dead will meet Christ first then those who are alive, at that time of his coming, will then "be changed" as in 1 Corinthians 15:51. The question that can be pondered is will there be a separation of those Christians that are alive, at that time, of their inner spirits/souls from their physical bodies and those spirits/souls rise to meet Christ the same as the souls/spirits of the dead will? In other words will there be a physical body ascension?
It could be argued that there will not be but that the Christians remaining, during those times, spirit/souls will be gone from their fleshly bodies leaving spiritless/soulless bodies behind. IF people suddenly left the earth, Christians were bodily resurrected to meet Christ then those "left behind" would surely know at that moment that something spectacularly and spiritually had happened and the world would be awakened to something happening. That could be though because in Revelation 6 it mentions people hiding away from God realizing that God's Judgement is upon them.
Lastly, as an interesting read, compare the events, spoken by Christ, in Matthew 24:4-29 to Revelation 6:1-17. Also compare Revelation 7:9-17 to what one might expect the appearance of the Rapture to be to someone that viewed it from a Spiritual realm (Heaven) and how it might look if described.
The above scripture references and comparisons are provided from a rapture timing perspective from the Pre-Wrath Rapture timing position which differs from the more prevalent, contemporary, opinion of Pre-Tribulation Rapture position so if you are a pre-tribulation timing advocate or believer then the above will not make sense nor can you read Revelation or Matthew 24 literally but have to take it figuratively or symbolically as there is no literal pre-tribulation scripture references, which is why many who advocate that position have major problems explaining their position with scripture or from scriptures such as 1 Thessalonians 5:4 and 2 Thessalonians chapter 2:1-12.
For those familiar with a previous member, Bill Gray, know he is a pre-Tribulationist advocate and I'm sure he wishes he could argue against what I have typed so if you wish to view what Pre-Tribulationist teach then either google "pre-tribulation" or see out Bill Gray's Facebook page where I'm sure he would gladly argue his position. AS it is there are FIVE views or the Rapture
- It doesn't exist, there is no rapture in scripture
- Pre-Tribulation - Rapture occurs before the tribulation period (that described in Matthew 24:4-29 and Revelation 6) The church will not enter into any of the Tribulation years
- Mid-Tribulation - Rapture occurs midway (3 1/2 years into the 7 year Tribulation period.)
- Post-Tribulation - Rapture happens at the end of the 7 year Tribulation period
- Pre-Wrath - Rapture happens somewhere into the 7 year Tribulation period BEFORE God's wrath (day of the Lord) happens, but after the beginning of the 7 year period that may say is signified with the Israeli 7 year peace agreement. The Church and Christians, alive at that time, will suffer through the first part of the Tribulation & Great Tribulation years a period of suffering under Antichrist.
Each Christian should read their scriptures and determine what they believe Scriptures teach and be confident and comfortable in what they believe.