Luke 3:15 gives us some points - the Jews were thinking in their
hearts John the Baptist may be the Christ. The descend of the Holy
Spirit on Jesus during baptism in full public view and the voice of
God convinces the Jews Jesus is the Christ (John has been speaking
of) sent by God.
In Acts, we witness the descend of the Holy Spirit (as promised by
Jesus)again to the apostles to convince everyone present the
apostles are sent by God.
imho.