Since the Catholic Church was not officially organized at this time, Paul could not have been referring to the CC when he mentioned "the obedience of faith" (or "obedience to the faith," KJV). He is talking to those "who also belong to Jesus Christ by calling: To all who are in Rome, loved of God, called His saints."
He's talking about believers in Jesus Christ--those who have faith in Him! Also note that Paul is calling these believers "saints."
Romans 1:1-7--Paul, a slave of Christ Jesus, called as an apostle and singled out for God’s good news — which He promised long ago through His prophets in the Holy Scriptures — concerning His Son, Jesus Christ our Lord, who was a descendant of David according to the flesh and who has been declared to be the powerful Son of God by the resurrection from the dead according to the Spirit of holiness. We have received grace and apostleship through Him to bring about the obedience of faith among all the nations, on behalf of His name, including yourselves who also belong to Jesus Christ by calling:
To all who are in Rome, loved by God, called as saints.
Grace to you and peace from God our Father and the Lord Jesus Christ.
the church was founded by Christ on Peter and the apostles and their successors Matt 16:18
Jesus Christ continues HIS ministry in His new covenant church thru Peter, the apostles, and their successors with the same mission, power, and authority!
Mt 16:18 Mt 28:19 Acts 1:17 acts 8:31 & 35 Lk 10:16 Jn 8:32 Jn 13:20 Jn 16:13
Jn 20:21-22 eph 2:20
All are called to be saints, in obedience yes but there is only one true faith as He says, and eph 4:5 Jude 1:3 not I read the Bible for myself (bibles were copied by hand before the printing press and rare and expensive and most people were illiterate until the 20 century) and make my own faith, or doctrines
we must be taught and instructed in the faith!
We must be taught by Peter, the apostles, and their successors! Matt 28:19 Jn 21:17
Matt 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Lk 1:4 That thou mightest know the certainty of those things, wherein thou hast been instructed.
Acts 8:30 And Philip ran thither to him, and heard him read the prophet Esaias, and said, Understandest thou what thou readest?
31 And he said, How can I, except some man should guide me? And he desired Philip that he would come up and sit with him.
unto the obedience of faith, Matt 28:19 also obey all I commanded Peter and the apostles