Paul's Inclusive Speech
Paul was speaking inclusively to the Thessalonians about this. As a fellow believer, he includes himself in his examples. This type of inclusion occurs in the Old Testament as well:
2 “The Lord also brings a charge against Judah,
And will punish Jacob according to his ways;
According to his deeds He will recompense him.
3 He took his brother by the heel in the womb,
And in his strength he struggled with God.
4 Yes, he struggled with the Angel and prevailed;
He wept, and sought favor from Him.
He found Him in Bethel,
And there He spoke to us—
-Hosea 12:2-4 (NKJV)
No one in Hosea's time was alive when God spoke to Jacob at Bethel, yet Hosea speaks inclusively in the last line of verse 4.
John Gill states the same in his commentary:
That we which are alive, and remain unto the coming of the Lord:
not that the apostle thought that he and the saints then in the flesh should live and continue till the second coming of Christ; for he did not imagine that the coming of Christ was so near, as is manifest from 2 Thessalonians 2:1-3 though the Thessalonians might take him in this sense, which he there corrects; but he speaks of himself and others in the first person plural, by way of instance and example, for illustration sake....
As does Thomas Coke in his commentary:
That we which are alive, &c.— Because here and elsewhere St. Paul speaks in the first person plural, and thereby seems to join himself with those who should be alive at Christ's second coming, when the dead are to be raised, and the living transformed,—some have too hastily concluded that he thought the day of the Lord to be just then at hand; and that he, and several of the Christians of that age, should be of the number of those who should (not die and be raised again, but) be transformed: but they are great strangers to St. Paul's [style] and manner, who have not observed in what a latitude he uses the word we; sometimes thereby meaning himself, and at other times himself and his companions; sometimes the Apostles, and at other times the Christians in general;—in some places the Jewish, and in other places the Gentile Christians....
There are only two groups that Paul is speaking of at the coming of the Lord: those who are alive and those who are dead. And as such, I think Charles Ellicott sums it well when he says:
We which are alive and remain.—Literally, We, (that is) the quick, those who are left over. There is not the least necessity for supposing from these words that St. Paul confidently expected the Advent before his death. Very likely he did, but it cannot be proved from this passage. Had the “we” stood alone, without the explanatory participles, it might have amounted to a proof, but not so now. [...] St. Paul is only picturing to imagination the scene of the Advent; and for any man it is far easier to imagine himself among the quick than among the dead at that moment.
The Brief Time Span Between the Two Thessalonian Letters
Paul writes his second letter to the Thessalonians shortly after the first, which was perhaps to help clarify things in his first letter. The start of both letters begin with the same greeting:
Paul, Silvanus, and Timothy,
To the church of the Thessalonians...
Silvanus is Silas, with Silas Σίλας being a contracted form of Silvanus Σιλουανός. Paul, Silas, and Timothy were together in Berea:
13 But when the Jews from Thessalonica learned that the word of God was preached by Paul at Berea, they came there also and stirred up the crowds. 14 Then immediately the brethren sent Paul away, to go to the sea; but both Silas and Timothy remained there. -Acts 17:13-14 (NKJV)
Paul is briefly separated from Silas and Timothy, but sent word for them to join him in Athens:
So those who conducted Paul brought him to Athens; and receiving a command for Silas and Timothy to come to him with all speed, they departed. -Acts 17:15 (NKJV)
Paul then leaves Athens and goes to Corinth:
After these things Paul departed from Athens and went to Corinth. -Acts 18:1 (NKJV)
Where all three are mentioned together again:
When Silas and Timothy had come from Macedonia, Paul was compelled by the Spirit, and testified to the Jews that Jesus is the Christ. -Acts 18:5 (NKJV)
Paul stays in Corinth for 1 year and 6 months:
And he continued there a year and six months, teaching the word of God among them. -Acts 18:11 (NKJV)
After which Paul departs for Syria with Priscilla and Aquila:
...Then he [Paul] took leave of the brethren and sailed for Syria, and Priscilla and Aquila were with him.... -Acts 18:18 (NKJV)
Paul, Silas, and Timothy are not mentioned being together again for the rest of Acts. While Timothy is mentioned as being with Paul again later in Acts 19:22 and Acts 20:4, Silas is not. 2 Thessalonians was written on behalf of Paul, Silas, and Timothy by Paul's own hand:
I, Paul, write this greeting with my own hand.... -2 Thessalonians 3:17 (ESV)
The salutation of Paul with my own hand.... - 2 Thessalonians 3:17 (NKJV)
and as such, there was a relatively short amount of time between when the first and second letters were written.
Paul used the word "we" in chapter 4 for illustrative purposes. For just a little later in the letter, Paul says concerning the day of the Lord:
But concerning the times and the seasons, brethren, you have no need that I should write to you. For you yourselves know perfectly that the day of the Lord so comes as a thief in the night. -1 Thessalonians 5:1-2 (NKJV)
There was no need to write to them about the times and seasons because they already knew such things. They knew of them because it was from Jesus' own words concerning His coming, such as what is recorded in Matthew 24. While a specific day or hour was not known, Jesus Himself gave general signs of the times that would indicate His return would be near. And as John Gill states, Paul did not imagine that the coming of Christ was so near, and though the Thessalonians might take him in this sense when he used the word "we," he corrects this possible misinterpretation of his words in his second letter to them shortly thereafter.