A Voice from the Past - Justin Martyr

For with what reason should we believe of a crucified man that He is the first-born of the unbegotten God, and Himself will pass judgment on the whole human race, unless we had found testimonies concerning Him published before He came and was born as man, and unless we saw that things had happened accordingly—the devastation of the land of the Jews, and men of every race persuaded by His teaching through the apostles, and rejecting their old habits, in which, being deceived, they had their conversation; yea, seeing ourselves too, and knowing that the Christians from among the Gentiles are both more
numerous and more true than those from among the Jews and Samaritans?

Justin Martyr, 100-165 AD, First Apology, Chapter LIII, (The Apostolic Fathers with Justin Martyr and Irenaeus, Philip Schaff, Wm. B Eerdmans Publishing, 2001, p. 242)

How important is the issue of fulfilled prophecy in showing the truth of Christ? What objections are there to this, and can they be met?