A great many contradictory reports were circulating in the year of Jesus’ death and after, and those that would’ve supported the claim that St. Peter & the apostles were making did not receive support from the religious teachers. The followers of Jesus would have appeared, to most, to be innovators with an interpretation about the Messiah that even his followers had not understood during his lifetime. Even the accurate reports would have been extremely difficult for any Jew to give credence to, since, as St. Paul said, he was preaching Christ crucified, to the Greeks (philosophers, intellectuals) foolishness and to the Jewish people, a rock for stumbling – and since placing a stumbling block in the path of a blind person is considered a sin in Jewish law, it would also be problematic: why would the Messiah, who ought to be unambiguously fulfilling the words of Moses and the prophets, claim at one time that the law of God would not pass away, and that to break the least of commandments would make one the least in heaven, and then, at other times, appear to view himself as authorized to obey a commandment or not.
As ever, faith would have required, not just demonstration, but also supernatural aid.