Titus 1:1-3

So yes, here we see that Paul is the author of this letter. Here he is also mentioning or asserting his apostleship, though, I don't see why he would need to assert that to Titus since he would already know it. However, he does mention it with regards to his goal or purpose, which is for the sake of faith of God's elect. He cares about the continuing faith and the bringing to faith of the elect. This means the preaching of the gospel to bring people to faith and the nourishing and encouragement of those who already believe. Paul goes on to talk about the promise of eternal life, which God made. God never lies, so we can trust that what he has said is true. He promised it long time ago and revealed it at the proper time. Some may wonder why he didn't reveal it sooner or to everyone. However, God in his great wisdom showed it at the right time, which we may not know or understand. At the very least, he is making it manifest through his servants, such as Paul. Through their preaching is it being revealed, by the instruction of the very God who saved them.