not to be...alarmed...that the day of the Lord has come.

(ESV) 2 Thess. 2:1 Now concerning the coming of our Lord Jesus Christ and our being gathered together to him, we ask you, brothers, 2 not to be quickly shaken in mind or alarmed, either by a spirit or a spoken word, or a letter seeming to be from us, to the effect that the day of the Lord has come. 3 Let no one deceive you in any way. For that day will not come, unless the rebellion comes first...

How do you make sense of these verses that Paul doesn't want them to think the day of the Lord has come because of the fact that a rebellion must come first. Won't the coming of the Lord be obvious with trumpets, etc?

I took a glance at another translation that makes more sense:
(KJV) 2 Thess. 2:1 Now we beseech you, brethren, by the coming of our Lord Jesus Christ, and by our gathering together unto him, 2 that ye be not soon shaken in mind, or be troubled, neither by spirit, nor by word, nor by letter as from us, as that the day of Christ is at hand. 3 Let no man deceive you by any means: for that day shall not come, except there come a falling away first...

The (or some) saints of Thessalonica were confused or misled by their own interpretations or the diversions of others, to the effect that the day of the Lord in some sense was a present reality, either had become fact or was "at/in the door" which was swinging open.

The latter idea might be used to blunt an objection someone raised, saying just as you have, "Hold it, I'm sure I remember Paul said/wrote it would be more noticeable than what we've experienced..."

The reassurance is coming from Paul--so don't think there was some intermediate letter (beside the authentic 1Thess.), containing some other statement or "correction" from the earliest face-to-face teaching.

In this letter Paul is basically reiterating, possibly with a few more words for clarity or exposition, what he had originally taught in the flesh, and sought to clarify in his first letter; and refuting the errors that had crept in.