Here is Titus 1.1 in the ASV (precursor to the NASB):
Paul, a servant of God, and an apostle of Jesus Christ, according to the faith of God’s elect, and the knowledge of the truth which is according to godliness.
The ESV’s interpretation of this is quite commonplace
Paul, a servant of God and an apostle of Jesus Christ, for the sake of the faith of God’s elect and their knowledge of the truth, which accords with godliness,
But I wonder if this interpretation is the most likely. In Ephesians 1 we learn that Paul is called as an Apostle “through the will of God” and that God’s will here is his redemptive plan for the ages, the mystery fulfilled in Christ. As Ridderbos points out, the content of Paul’s Gospel is the announcement of the fulfillment of this mystery. So we have:
Paul, an apostle of Christ Jesus through the will of God… In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, which he lavished upon us, in all wisdom and insight making known to us the mystery of his will, according to his purpose, which he set forth in Christ as a plan for the fullness of time, to unite all things in him, things in heaven and things on earth. In him we have obtained an inheritance, having been predestined according to the purpose of him who works all things according to the counsel of his will
In Paul’s first letter to the Corinthians, we have the content of this Gospel recorded in what seems to be a standard formula. Notice what the content includes:
Now I would remind you, brothers, of the gospel I preached to you, which you received, in which you stand, and by which you are being saved, if you hold fast to the word I preached to you—unless you believed in vain. For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, that he was buried, that he was raised on the third day in accordance with the Scriptures, and that he appeared to Cephas, then to the twelve. Then he appeared to more than five hundred brothers at one time, most of whom are still alive, though some have fallen asleep. Then he appeared to James, then to all the apostles. Last of all, as to one untimely born, he appeared also to me.
Obviously, when Paul speaks of himself, he is hardly using public Church formulas. But it still seems clear that the Gospel includes some statements about how the Gospel is being faithfully transmitted under God’s direct care and according to his plan.
In which case, it seems to me perfectly possible that Paul would speak of “the faith of God’s elect” and “the knowledge of the truth,” as a charter that acknowledges his calling. After all, the knowledge of the truth is “according to godliness” which reminds us of the confession in First Timothy 3.16 which includes affirmations that Christ was
seen by angels [messengers],
proclaimed among the nations,
believed on in the world