You are correct the passage in Matthew speaks of what happens after the Great Tribulation.
But it is not saying the rapture will happen after the Great Trib. The passage in Matthew is speaking of when Jesus Christ comes back with His saints to rule & reign. Jesus Christ's second coming to Earth when His feet touch the Mt. of Olives and split it in two. When Jesus comes back for the Bride, We MEET Him in the Air.
Note:
"And he shall send his angels with a great sound of a trumpet, and they shall gather together his elect from the four winds, from one end of heaven to the other."
Note here: "Gathering elect from one end of heaven to the other" does not say gathering from earth. The elect are already in heaven, therefore, the rapture, dead in Christ and those who are alive and remain shall be caught up to be with Him, means it happened already as described in I. Thes.
Yes, there have been famines, earthquakes, wars, rumors of war, pestilence since the beginning. But we haven't seen 1/3 of the earth destroyed yet or the moon turn to blood as will happen in the Great Tribulation. We haven't seen the abomination of abominations happen in the 3rd Solomon's Temple at Jerusalem, either, yet. We haven't seen total world wide identification, yet, though it is close.
We don't see people fleeing to Petra, yet. Those who finally believe during the Great Trib & become saved, accepting Jesus Christ IS the Son of God, Messiah, after all, will be beheaded. Israelis who flee & hide in the Rock City of Petra (in present-day Jordan) will find the Bibles that pre-trib Believers have hidden there for them to find with the Gospel.
All who wait & become Christians after the Rapture will be beheaded if found. All who manage to endure to the end (without taking the Mark of the Beast) & not found by the Anti-Christ worldwide government will be physically (bodily) saved. We haven't seen the worldwide mark yet that will have to be worn in the hand or forehead in order to buy & sell, either.
And I personally believe the vivid description of the great harlot/Babylon described in Rev. 18 could be NYC. On 09/11, the description in Rev. 18 fit NYC like a glove. The whole world was in turmoil. The merchants (Wall St./stock market) was in shock. The global economy was affected. It was carnage with smoke as described in Rev. 18. But it wasn't that particular event though perhaps it was a foretaste of that final description in Rev. 18. I don't know. I won't be around when that happens, I'll be with Jesus wearing my glorified body.
And no, I don't place this doctrine or beliefs on Hal Lindsay or the Left Behind series, etc. I have studied this for more than 40 years & have believed this for nearly as long, based on Bible Prophecy, comparing Scriptures with Scriptures, OT and NT. (KJV, BTW)
But of course if one doesn't believe in both a Literal and Figurative Interpretation in Bible prophecy, then nothing anyone can post here will make a difference. So.....we'll wait & see. I'm listening for the sweet trumpet sound.
The rapture will be a surprise only to those who aren't looking for it to come.....Some of us wake up & say, "Lord, are you coming today? We're ready to go! This old wicked planet is NOT our home!"
"There is going to be a meeting in the air, in the sweet, sweet by & by....
I am going to meet you, meet you there, in that land beyond the sky..."
Selah & Shalom.