If we consider the origins of Christianity there is evidence that it was very diverse. This makes it extremely difficult to objectively prove any form of authority to be valid based upon history alone. If length of continuous history alone is any form of proof then Catholic and Orthodox forms have strong claims based upon their long recorded history. That doesn’t however prove they are the original or true forms and a common Protestant claim has been that they became apostate or corrupted by time rather than being preserved by it. Some restorationist churches, such as the Christadelphians, have gone further and claimed ALL basic doctrines as well as practices were corrupted with time. Some have claimed restoration as a result of the leading of the Holy Spirit, some such as the Mormons claim additional revelations, some such as the Christadelphians have claimed rediscovery based upon the theological studies of the Bible by their founders.
History shows that Christianity has also had purely esoteric forms as well as exoteric forms. An exoteric one claims a basis in historical fact. Most Christian denominations are based upon exoteric claims. In other words Jesus existed as a real man on the earth, he was crucified on a real cross and rose from the dead. We find in the Bible there were people who did not believe Jesus came in the flesh. They were known as Gnostics and they were persecuted as heretics and only some of their writing survive. Throughout history various esoteric forms have re-emerged, usually based upon claims of inner enlightenment. Inner enlightenment however isn’t limited to esoteric forms and most forms of Christianity have also believed in some form of being led by the Spirit too. The Christadelphians are an exception to this.
As noted by Christadelphians the difficulty with an esoteric basis of authority, such as being led by the Spirit, is that whilst it may be objective to the person having the experience it can seem subjective to other people. The Catholic Church claims the Holy Spirit works through it to ensure the preservation of the church, the Jehovah’s Witnesses claim their leadership (“the faithful servant”) is similarly guided, so do Pentecostals and the Mormons claim so was their founder. This does not of course mean God does not draw or guide, it simply means many who claim it must not in fact be so guided.
Early Christian writings as well as the Bible show early Christians regarded the Old Testament as scripture. The New Testament also shows the writers quoted liberally from the Old Testament to validate their claims. They sought to show that it fitted, although they often spiritualised the quotations they took from the Old Testament. Jesus is also said to have demonstrated his authority by the things that he did such as healing the sick, raising the dead and casting out demons. The early Christians also made similar claims. In their terms authority was based upon the obvious outward working of God. Since we do not see that display in most churches claiming some form of authority we can rightly say they do not have apostolic authority. In fact this lack of seeming power is the No. 1 problem Christianity today has to back up its claims.