A) 1st century BCE
B) 1st century CE prior to the First Jewish-Roman War
C) After the First Jewish-Roman War.
I've listed these in chronological order, but I'll address option B first, as its the consensus position.
B> Arguments in favor of the Pauline letters having originated in the first century, prior to the First Jewish-Roman War:
1) Tradition - enough said
2) Aretas reference in 2 Cor 11 being Aretas IV - who reigned from 9 BC to 40 CE.
3) Mentions of going to Jerusalem in Galatians, 1 Cor and Romans imply a functioning city not under occupation.
4) The general lack of overt discussion about the war or the destruction of the temple. Some passage that imply strongly the war has not yet occurred, e.g. 1 Cor 10.
5) The Gospel of Mark can be viewed as preface to the Pauline letters. By setting the story during the reign of Pilate, the writer implies that Paul's ministry follows shortly after.
C> Arguments in favor of the Pauline letters having originated after the First Jewish-Roman War:
1) There is no real account of Paul or these letters until the 2nd century. References to Paul or Pauline letters are often dated to the mid-late 1st century, such as 1 Clement, HOWEVER, these datings are highly dubious. They are based on assumptions of circular reasoning. The first time we know for sure that people are aware of Paul is the middle of the 2nd century via Marcion.
2) There is little or no evidence of the supposed communities visited by Paul prior to the war. Dating Paul's ministry to 40-60 CE implies that these communities existed for 100 years prior to the "breakout" of Christianity in the 2nd century. Where are these community's traditions? Why do they seem to have such little impact on 2nd century Christianity?
3) The Pauline message fits perfectly into a world in which the Temple had been destroyed. "Paulinism" judges the priesthood harshly, it opposes circumcision, it opposes the Law, it identifies the body as the Temple of God, not the Temple in Jerusalem. Destruction of the Temple, in accordance with Jewish traditions, would be seen as evidence that the status quo of the Temple priesthood was flawed and displeased God. It would have been seen as evidence that the priestly interpretation of the scriptures was incorrect, thus providing the opening for new interpretations.
4) Some passages do imply that the Temple had been destroyed and that the war had happened. Examples:
25 Now this Hagar is Mount Sinai in Arabia and corresponds to the present Jerusalem, for she is in slavery with her children. 26 But the Jerusalem above is free; she is our mother.
14 For you, brethren, became imitators of the churches of God in Christ Jesus that are in Judea, for you also endured the same sufferings at the hands of your own countrymen, even as they did from the Jews, 15 who both killed the Lord Jesus and the prophets, and drove us out. They are not pleasing to God, but hostile to all men, 16 hindering us from speaking to the Gentiles so that they may be saved; with the result that they always fill up the measure of their sins. But wrath has come upon them to the utmost.
1 Thess 2 :14-16 is suspected of being an interpolation due its apparent reference to the war.
6 Yet we do speak wisdom among those who are mature; a wisdom, however, not of this age nor of the rulers of this age, who are passing away; 7 but we speak God’s wisdom in a mystery, the hidden wisdom which God predestined before the ages to our glory; 8 the wisdom which none of the rulers of this age has understood; for if they had understood it they would not have crucified the Lord of glory;
Is this referring to those who brought about the destruction of the Temple?
1Brethren, my heart’s desire and my prayer to God for them is for their salvation. 2 For I testify about them that they have a zeal for God, but not in accordance with knowledge. 3 For not knowing about God’s righteousness and seeking to establish their own, they did not subject themselves to the righteousness of God.
11 I say then, God has not rejected His people, has He? May it never be! For I too am an Israelite, a descendant of Abraham, of the tribe of Benjamin. 2 God has not rejected His people whom He foreknew. Or do you not know what the Scripture says in the passage about Elijah, how he pleads with God against Israel? 3 “Lord, they have killed Your prophets, they have torn down Your altars, and I alone am left, and they are seeking my life.” 4 But what is the divine response to him? “I have kept for Myself seven thousand men who have not bowed the knee to Baal.” 5 In the same way then, there has also come to be at the present time a remnant according to God’s gracious choice. 6 But if it is by grace, it is no longer on the basis of works, otherwise grace is no longer grace.
7 What then? What Israel is seeking, it has not obtained, but those who were chosen obtained it, and the rest were hardened; 8 just as it is written,
“God gave them a spirit of stupor,
Eyes to see not and ears to hear not,
Down to this very day.”
9 And David says,
“Let their table become a snare and a trap,
And a stumbling block and a retribution to them.
10 “Let their eyes be darkened to see not,
And bend their backs forever.”
11 I say then, they did not stumble so as to fall, did they? May it never be! But by their transgression salvation has come to the Gentiles, to make them jealous. 12 Now if their transgression is riches for the world and their failure is riches for the Gentiles, how much more will their fulfillment be! 13 But I am speaking to you who are Gentiles. Inasmuch then as I am an apostle of Gentiles, I magnify my ministry, 14 if somehow I might move to jealousy my fellow countrymen and save some of them. 15 For if their rejection is the reconciliation of the world, what will their acceptance be but life from the dead? 16 If the first piece of dough is holy, the lump is also; and if the root is holy, the branches are too.
Why does Paul ask if God has rejected his people? Why would people think that? Because of the destruction of the Temple? What is their transgression?
1 Every person is to be in subjection to the governing authorities. For there is no authority except from God, and those which exist are established by God. 2 Therefore whoever resists authority has opposed the ordinance of God; and they who have opposed will receive condemnation upon themselves.
Is this issue being raised because of the outcome of the war? The Jews tried to reject the governing authority. They were judged harshly.
A> Arguments in favor of the Pauline letters having originated in the 1st century BCE:
1) The Aretas reference in 2 Cor 11 more closely resembles Aretas III - who reigned from 87 - 62 BCE
2) Many aspects of the Pauline letters seem to align with events from the 1st century BCE. See: viewtopic.php?f=3&t=5464
3) The Pauline letters imply that something has happened which shows that the Jews have been judged harshly by God, yet overall the letters do seem to imply that the Temple is unharmed. Might the judgement against the Jews be the loss of the Hasmonean kingdom to Pompey in 63 BCE? Might Paul's ministry have been prompted by the integration of the Hasmonean kingdom into the Roman Empire?
4) Philippians 4:22 "All the holy ones greet you, especially those of Caesar’s household." - Caesar Augustus?
While these are supposed to be arguments in favor, I would point out that if A were true it would imply that these groups Paul visited existed for 200 years prior to the 2nd century explosion of Christianity. Surely they would have had something to say about it by then eh?
I'm sure I haven't covered all the possible arguments in favor of these datings, nor the arguments against them.