I believe the issue is not the existence of photographs or documents, but reasonable testimony. For example, if we believe Jesus lived, and we believe Jesus ordained Peter, Matthew, and others; and persons named in the New Testament who identified as having been instituted by those Apostles as bishops, teachers, elders, presbyters, etc.; and besides those specified central Apostles - second only to Jesus Christ - and there were another sort of general apostles - “first apostles, second prophets, third teachers” (1 Corinthians 12:28), as there also were general prophets ("Now in the church at Antioch there were prophets " - Acts 13:1), and not as in the Mormon Church - “first a single Prophet, second Counselors to the Prophet, third Apostles . . . and not until around seventh place teachers…” In the New Testament, and corroborated by historical documents, we see Jesus, his Apostles, their disciples, and we read later that their successors were documented by church writers and historians. Over the passage of years, many of those have been lost, and for some it seems impossible to trace the transfer of authority from one generation of church leaders to the next. But other documents refer to them, and some documents contain partial lists. There is sufficient evidence in the reports of historians, and in the very fact that where a church is identified in the New Testament, such as at Rome or Antioch or Corinth, there is today a church there so that one could hardly imagine that there was no continuous bishopric in those places: to persuade non-Christians that there was a continuity of office. Continuity of office was indeed broken in some areas, but then reestablished through the authority of responsible bishops whose line of succession had not been broken or had been broken and similarly restored.
For the LDS Church, the situation is notably different. Jesus Christ was not alive in the sense he was 2000 years ago. He did not call twelve different men separately, bring them together, teach them personally. walk with and minister to them and let them see him minister to others. He was not opposed by local ministry - neither by American Jews nor by rival Christians. He was not brought to trial by Jewish leaders, nor persecuted by Romans. There was one man who claimed that Jesus had appeared to him. That man did not follow Jesus as the latter walked the land ministering and teaching. That man claimed personal (private, nonpublic) revelation (a type of teaching), and that man passed on that alleged teaching. Jews and Romans knew of Jesus, some met him. They met his Apostles, who could tell them what Jesus had taught them, and what they had seen Jesus do. Mormon apostles cannot tell what Jesus taught them, they are afraid even to ask each other if they even saw Jesus! Mormon apostles cannot tell what Jesus did in front of them, to feed thousands or teach thousands, because they never personally saw that, neither yesterday nor today.
It is true that a Mormon can show a list of names purporting to be his line of authority, from whoever ordained him all the way back to Jesus. But beyond Joseph Smith, there is no corroborating witness that Jesus even appeared to ordain Joseph Smith as an Apostle. Jesus appointed and laid his hands on twelve Apostles two thousands years ago. He allegedly laid his hand on one man’s head, who was called “First Elder” not “First Apostle.” I do not believe Jesus ordained anyone 2000 years ago to be a Prophet. Joseph Smith may claim to have been ordained a prophet by Jesus. But when has a Prophet’s role included ordaining apostles? - among LDS, yes; but in Jesus’ time and in Jesus’ way, no.
There may be exceptions to what I have said,
but the general principles are true.