Yes his church founded in the apostles that would make it “apostolic”!
Christ Church was founded on the belief of the Apostles and the Prophets
Mat 16:13 When Jesus came into the coasts of Caesarea Philippi, he asked his disciples, saying, Whom do men say that I the Son of man am?
Mat 16:14 And they said, Some say that thou art John the Baptist: some, Elias; and others, Jeremias, or one of the prophets.
Mat 16:15 He saith unto them, But whom say ye that I am?
Mat 16:16 And Simon Peter answered and said, Thou art the Christ, the Son of the living God.
Mat 16:17 And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.
Mat 16:18 And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.
Act 11:25 Then departed Barnabas to Tarsus, for to seek Saul:
Act 11:26 And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.
Eph 2:19 Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God;
Eph 2:20 And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;
Eph 2:21 In whom all the building fitly framed together groweth unto an holy temple in the Lord:
Eph 2:22 In whom ye also are builded together for an habitation of God through the Spirit.
Jesus never said He built His Church on Peter, even though many Catholics are taught that Peter was the first Pope, but that the Apostles and the Prophets who were first called Christians in Antioch as the Holy Spirit revealed to all of them that Jesus is the Son of the living God and with that belief Christ established His true Church being the cornerstone that holds all things together. Jesus is the cornerstone for everything He and the Father dreamed up at the beginning of time being the firstborn of all creation. Colossians 1:15-19; 1Peter 2:4-6.