Each is Called Upon to Justify belief in the Other
One reason we get into this predicament is that it was the apostle Paul's usual practice to evangelize the Jews by reasoning with them from the Scriptures that Jesus is the Christ. The Jews however believed those Old Testament Scriptures to be inspired and authoritative. Paul had a very different approach addressing Gentiles (Acts 14 & 17). His theology remained biblical without presuming that Bible texts should be the final court of appeal.
A second reason is that we do not think clearly about the object of Christian belief. We should be asking people to put their trust in a person, not a book. 'Believe in the Lord Jesus and you will be saved' (Acts 16:31).
Christians regard the Bible as the revealed word of God ultimately because we conclude that Jesus himself had that view of Scripture, and discipleship means intellectual as well as moral submission to his kingly rule. 'You call me Teacher and Lord. You are right, for so I am' (John 13:13). Jesus insisted repeatedly 'A student is not above his teacher... it is enough for the student to be like his teacher' (eg Matt 10:24). Trusting the Scriptures is a proper consequence of first of all submitting ourselves to Jesus and becoming his disciples. It is Jesus whom we are asking people to trust and obey.
Our Argument is Linear not Circular
The force of our argument about Jesus flows from the apostolic testimony about him recorded in the collection of first century documents which we call the New Testament. Our appeal to them is not as authoritative Scripture, but as credible historical documents.
In other words we start where they are. They cannot reasonably deny that these documents were written in the first century. We can produce compelling evidence that these writings have survived the centuries essentially as they were written.
The documents describe the amazing figure of Jesus of Nazareth, who gave the world a body of teaching which is there for everyone's evaluation. He is described as an exemplary character who practised what he preached. He is said to have performed amazing deeds, and his sayings are shot through with the most extraordinary claims he made about himself. The events of his life are said to have climaxed not only in his death but in his resurrection.
The whole saga, because of the importance of his teaching, the example of his character, his astonishing claims and the impact he had made on the world's stage, demands evaluation from every thoughtful responsible person. They may conclude that the whole story is invention, but history is not on their side.
Our task is to argue from history that Jesus is the Son of God.
(For an example, see the booklet 'The Greatest Person?')