Early Christians did not counterfeit the prophesies about Christ. The first century Jewish understanding of the messianic prophecies and the Christian’s claims about those prophecies are not far apart as Arlie J. Hoover notes in his book Dear Agnos: Letters to an Agnostic in Defense of Christianity (pp. 209-210).
The best proof that Christians didn’t invent the messianic argument is that long before Christ the Jews had a body of messianic literature that agrees substantially with what Christians said of Christ. Both Jew and Christian expected that the Messiah would be a descendent of Judah and David, be born at Bethlehem, be filled with God’s Spirit, be a king and priest, rule with justice, bestow peace, have a glorious and enduring kingdom, subject the gentile nations to his law, and so on.
What some of the Jews in their unbelief failed to recognize was the fact that along side the passages that depicted the glory of the Messiah were those darker passages that also depicted his death and resurrection.
The important point to note is that the prophesies were written before the birth of Jesus. We can know that from the Jewish literature of the time, the manuscripts of the Old Testament that date before the first century A.D., and the translation of the Old Testament into Greek which dates from 200 to 100 B.C. We do not have to worry about the criticism that would claim the prophesies were written after Christ to make it look like Jesus had fulfilled them.
That means the messianic prophecies need to be taken seriously as evidence about Jesus. The number of prophecies to consider are numerous. James E. Smith in his What the Bible Teaches about The Promised Messiah treats 73 prophecies. Alfred Edersheim listed 456 passages which were interpreted as Messianic in ancient Jewish literature. J. Barton Payne in his Encyclopedia of Biblical Prophecy identified 1239 predictions in the OT (6,641 verses) of which 127 (3,348 verses) were personal Messianic predictions.
Josh McDowell in Evidence that Demands a Verdict (p. 167) gives an interesting statement on the odds of Jesus fulfilling the various Old Testament prophecies. McDowell notes that one mathematician calculated the odds of fulfilling eight key prophecies as 1 chance in 100,000,000,000,000,000. The fulfillment of these prophecies by Jesus is evidence of God’s intervention and omniscience. They are an important part of the evidence to authenticate Jesus as God’s promised Messiah.