Then what you are doing is making unwarranted assumptions and reading you own ideas into scripture which are not there. The timeline in Acts indicates Paul was left on his own in Athens.
So you admit that "we" in 1 Thes 2:2 is just Paul and Silas who suffered in Philippi. If you say Paul is not using the word "we" loosely, but that he uses it consistently to refer to the same people, then your own logic proves that Timothy at least was not an apostle. Verses 1 and 2 are the same sentence, so the "our coming to you" in v1 must also be just Paul and Silas; and the other "we" in verse 2 must also be just Paul and Silas, the "we .... who speak to you" (otherwise Paul's grammar is completely up the creek). So if it is Paul and Silas who "came to you" and "spoke to you" then, as your logic would dictate, the "we" in the following verses must also be just Paul and Silas. So Timothy was not an apostle in v6. (But we knew that anyway from the way Paul referred to Timothy in the opening of his other epistles - "Paul, an apostle of Christ Jesus...and Timothy our brother”).
The Pulpit commentary is right, Timothy was in Athens, and was sent to Thessalonica in 1 Thes 3:2. The so the "we" who were left behind in 1 Thes 3:1 definitely does not include Timothy. The timeline in Acts would indicate that it doesn't include Silas either.
Here are a couple of other more up-to-date commentaries:
Wayne Grudem - Systematic Theology
a. Qualifications of an Apostle: The two qualifications for being an apostle were (1) having seen Jesus after his resurrection with one’s own eyes (thus, being an “eyewitness of the resurrection”), and (2) having been specifically commissioned by Christ as his apostle.4
The fact that an apostle had to have seen the risen Lord with his own eyes is indicated by Acts 1:22, where Peter said that person to replace Judas “must become with us a witness to his resurrection.” Moreover, it was “to the apostles whom he had chosen” that “he presented himself alive after his passion by many proofs, appearing to them during forty days” (Acts 1:2–3; cf. 4:33).
Paul makes much of the fact that he did meet this qualification even though it was in an unusual way (Christ appeared to him in a vision on the road to Damascus and appointed him as an apostle: Acts 9:5–6; 26:15–18). When he is defending his apostleship he says, “Am I not an apostle? Have I not seen Jesus our Lord?” (1 Cor. 9:1). And when recounting the people to whom Christ appeared after his resurrection, Paul says, “Then he appeared to James then to all the apostles. Last of all, as to one untimely born, he appeared also to me. For I am the least of the apostles, unfit to be called an apostle” (1 Cor. 15:7–9).
These verses combine to indicate that unless someone had seen Jesus after the resurrection with his own eyes, he could not be an apostle.
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Others have been suggested as apostles. Silas (Silvanus) and sometimes Timothy are mentioned because of 1 Thessalonians 2:6: “though we might have made demands as apostles of Christ.” Does Paul include Silas and Timothy here, since the letter begins, “Paul, Silvanus, and Timothy” (1 Thess. 1:1)?
It is not likely that Paul is including Timothy in this statement, for two reasons. (1) He says just four verses earlier, “we had already suffered and been shamefully treated at Philippi, as you know” (1 Thess. 2:2), but this refers to the beating and imprisonment which happened just to Paul and Silas, not to Timothy (Acts 16:19). So the “we” in verse 6 does not seem to include all of the people (Paul, Silvanus, Timothy) mentioned in the first verse. The letter in general is from Paul, Silas and Timothy, but Paul knows that the readers will naturally understand the appropriate members of the “we” statements when he does not mean to include all three of them in certain sections of the letter. He does not specify “—that is, Silas and I—had already suffered and been shamefully treated at Philippi, as you know,” because the Thessalonians will know who the “we” are that he is talking about.
(2) This is also seen in 1 Thessalonians 3:1–2, where the “we” certainly cannot include Timothy:
Therefore when we could bear it no longer, we were willing to be left behind at Athens alone, and we sent Timothy our brother and God’s servant in the gospel of Christ, to establish you in your faith and to exhort you. (1 Thess. 3:1–2)
In this case, the “we” refers either to Paul and Silas, or else just to Paul alone (see Acts 17:14–15; 18:5). Apparently Silas and Timothy had come to Paul in Athens “as soon as possible” (Acts 17:15)—though Luke does not mention their arrival in Athens—and Paul had sent them back to Thessalonica again to help the church there. Then he himself went to Corinth, and they later joined him there (Acts 18:5).
It is most likely that “We were willing to be left behind at Athens alone” (1 Thess. 3:1), refers to Paul alone, both because he picks up the argument again in verse 5 with the singular “I” (“When I could bear it no longer, I sent that I might know your faith,” 1 Thess. 3:5), and because the point concerning extreme loneliness in Athens would not be made if Silas had stayed with him.8 In fact, in the previous paragraph, Paul means “I,” for he says, “We wanted to come to you—I, Paul, again and again—but Satan hindered us” (1 Thess. 2:18). Apparently he is using “we” more frequently in this epistle as a courteous way of including Silas and Timothy, who had spent so much time in the Thessalonian church, in the letter to that church. But the Thessalonians would have had little doubt who was really in charge of this great mission to the Gentiles, and on whose apostolic authority the letter primarily (or exclusively) depended.
So it is just possible that Silas was himself an apostle, and that 1 Thessalonians 2:6 hints at that. He was a leading member of the Jerusalem church (Acts 15:22), and could well have seen Jesus after his resurrection, and then been appointed as an apostle. But we cannot be very certain.
The situation with Timothy is different, however. Just as he is excluded from the “we” of 1 Thessalonians 2:2 (and 3:1–2), so he seems to be excluded from the “we” of 1 Thessalonians 2:6. Moreover, as a native of Lystra (Acts 16:1–3) who had learned of Christ from his grandmother and mother (2 Tim. 1:5), it seems impossible that he would have been in Jerusalem before Pentecost and would there have seen the risen Lord and come to believe in him, and then suddenly have been appointed as an apostle. In addition, Paul’s pattern of address in his letters always jealously guards the title “apostle” for himself never allowing it to be applied to Timothy or others of his traveling companions (note 2 Cor. 1:1; Col. 1:1: “Paul, an apostle of Christ Jesus...and Timothy our brother”; and then Phil. 1:1: “Paul and Timothy, servants of Christ Jesus”). So Timothy, as important a role as he had, should not rightly be considered one of the apostles.
John Stott - The Message of 1 & 2 Thessalonians [Intervarsity, 1994], 71-74.
Three points may be made. First, Luke in Acts is quite clear that Paul was the leader of his mission team. Silas had been chosen to replace Mark, and Mark had been only a "helper' [cf. Acts 13:5; 15:37ff]. Timothy, though much loved, was clearly a junior [Cf. Acts 16:1ff]. Luke does indeed couple 'Paul and Silas' as fellow prisoners [cf. Acts 16:19, 22, 25, 29), Roman citizens [cf. Acts 16:38], and co-labourers [cf. Acts 16:40; 17:4]. Yet he makes it clear that Paul did the preaching, in both the Thessalonian and the Berean synagogues [cf. Acts 17:2-3, 11]. If, then, he was the leading preacher, it is all but certain that he was the leading writer (of 1 Thessalonians] too.
Secondly, Paul was an Apostle, whereas Silas and Timothy were not. True, Silas was a leader in the Jerusalem church, an official delegate of the Jerusalem Council and a Prophet [cf. Acts 15:22, 27, 32], but he is never named an Apostle. Nor is Timothy. In fact, in later letters Paul deliberately distinguishes himself from Timothy in this respect by writing 'Paul, an Apostle of Christ Jesus and Timothy our brother' (cf. 2 Cor 1:1; Col. 1: 1; cf. 1 Cor 1: 1; Phm 1).
It is in the light of this that we must understand the surprising expression 'as Apostles of Christ we could have been a burden to you' (1 Thes. 2:6b). Either Paul was using the word 'Apostles' here in its broader sense of 'missionaries' (cf. Acts 14:4, 14; 2 Cor 8:23; Phil 2:25], or he was referring to himself as the Apostle but was forced by grammar to write 'Apostles' in the plural, in order to be in apposition to 'we' (rather like 'we were left alone [monoi, plural]' in 3:1).
Thirdly, there are many examples in Paul's other letters where he moves from "I" to "we" without appearing to change the identity of the subject. ... his use of "we" is never incompatible with his leadership role in the mission team and never lessens his authority as an Apostle of Jesus Christ.
