There are a number of Biblical sources that support the Church’s teachings are backed by God. Here is one:
Matthew 16: 13 When Jesus came into the region of Caesarea Philippi, He asked His disciples, saying, “Who do men say that I, the Son of Man, am?”
14 So they said, “Some say John the Baptist, some Elijah, and others Jeremiah or one of the prophets.”
15 He said to them, “But who do you say that I am?”
16 Simon Peter answered and said, “You are the Christ, the Son of the living God.”
17 Jesus answered and said to him, “Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven. 18 And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it. 19 And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.”
In other places in the New Testament, Jesus explained His thoughts to His Apostles in private that are not recorded in the New Testament. Jesus also promised to send the Holy Spirit to REMIND them of all that He taught. And Jesus said He would be with them through the end of time.
And in every encyclical I have read issued by a Pope, successors of St Peter, the teachings are well footnoted to the Bible.
If we believe that Jesus Christ is indeed the living Son of God, we do well to do our best to understand and follow the Church’s teachings coming directly from the Bible. Christ gave no other Church the authority to teach in His Name.