No. (and I did explain this somewhere in this thread, or the related thread... before you arrived here at CC... so my apologies for the "repeat"... I'll make this brief)...
The text does not inform us that "*[missing] the Rapture" was "on their distraught / troubled / shaken minds" [or even in a "potential" sense, so that Paul found it necessary to address this letter to them]...
Sorry, that's exactly what the text informs us. Paul suggested that they were wrong in their expectation of Christ's Coming and the Rapture. They had already been taught about the Rapture in 1 Thes 4.
2 Thes 2.5 Don’t you remember that when I was with you I used to tell you these things?
No, Paul, in this 2nd letter, is BRINGING "the Rapture" [Subject] TO BEAR on the matter... the matter being "the thing that the false conveyors of v.2 were purporting..."
The false conveyors were purporting that Christ's Coming and the Rapture had already taken place, which was the gathering of Christians to Christ. False prophets and false teachers were pretending to be a form of Christ's Kingdom on the earth, which was beginning to be revealed. Paul was calling this "nonsense."
[which was a DIFFERENT Subject--one that was both TROUBLING and PERFECTLY-REASONABLY-SENSIBLY commensurate with their PRESENT and ONGOING "persecutions and tribulations ye endure" per 1:4; not something that WASN'T *reasonable* and which [/such a thing would have] displayed ABSOLUTELY ZERO EVIDENCE of being even remotely so...]
The Thessalonians well knew they were suffering tribulations, which was normal for Christianity at that time. Jesus had clearly warned his apostles that they would experience resistance to the Gospel from the world. None of this has anything to do with the expectation, by the Thessalonians, that Jesus had come. They thought Jesus had come simply because someone was claiming that, and so Paul warned against these claims, whether spoken or in writing, no matter who was doing the claiming.
Your entering into the discussion information about tribulations has nothing to do with the subject. All the churches knew they experienced opposition from the world, and beliefs about Christ's return were distinct from this. They did, undoubtedly, know about Daniel's prophecy, in ch. 7, that the Man of Sin had to come 1st. So they may have viewed the tribulations of their time as this Antichristian revelation, against which the Kingdom was now rising on earth to oppose it.
Paul warned them that Antichrist was an actual man who would fulfill the prophecies of Daniel--that's where Paul got his information from. He would oppose God until the Son of Man descends from heaven to destroy him.
The part you put about [them purporting] "that the Tribulation had already started"... yes... "2 ...[purporting] that the Day of the Lord IS ALREADY HERE / IS PRESENT [PERFECT INDICATIVE]"...
(and 1Th5:2-3 tells us they already "KNOW PERFECTLY" the manner of its ARRIVAL... LIKE the INITIAL "birth PANG [SINGULAR]" that COMES UPON a woman... Like Jesus had already talked about...)
"The day of the Lord" consisting of BOTH "a period of time of JUDGMENTs... as well as a period of time of BLESSINGs"
You are defining the "day" Paul was speaking of by other applications of the "day of the Lord" in other Scripture passages, thus conflating them. That is an illegitimate manner of interpretation. It may or may not be true, but it is not a legitimate manner of interpreting Scripture passages.
If you want to define the "day" Paul is speaking of you must interpret it by its immediate context in 2 Thes 2. And the context there is the coming of Christ for his Church, ie the Rapture. We are not to expect that literal day, which is the day Antichrist is destroyed, unless first a literal Antichrist appears. Until that time we are not to expect a final Kingdom appearance and deliverance.
So don't define the "day of the Lord" as both judgment and salvation because it is used as such elsewhere. In this passage, the context is the "Rapture." We are not to expect that until Antichrist is destroyed at the coming of Christ. All who claim that there are manifestations of Christ's coming now, or manifestation of Christ's Kingdom experiencing victory now, present a lie, and we are to reject it. This is the message of the book.