What do you mean by "first-hand?" Matthew was written at least 10 years after the Ascension, Mark, 25 years after the Ascension, Luke later than that, and John later than that. St. Paul wrote his first letter in the 50's. The Christian Word of God was proclaimed by oral means for at least 10-20 years.
It is first hand testimony from witnesses who had heard, which had seen with their eyes, which had looked at and their hands had touched the Word of Life Jesus Christ (1 John 1:1).
Sure the written testimonies were written after the fact, but it would be no different to a person writing a witness statement for a court proceeding some several months or even several years after the fact.
Religious institutions have written doctrine as an extension to the FACT of first hand eye witness account, by making claims as if it is the FACT that has been both endorsed by the first hand eye witnesses who are the disciples and that it had been authorised by the first hand eye witnesses as an authority equal to or greater than them.
Once a religious institution takes it upon themselves to act in a legalistic pharisaical spirit, that is in the image of their mother relgious institution the pharisaical institution that Paul abandoned, then they make fraudulent claims based on hearsay by falsely saying that that their doctrine is both endorsed and authorised by the disciples themselves.
We have to reject their claims as baseless and since no evidence can be provided by those relgious institutions making those claims, that the apostles both endorsed their doctrine and authorised them to be of equal or greater authority than them, then we must again reject doctrine that is outside of the details of the written first hand testimony of the disciples who established the faith and who had completely taught what was required for one to be saved.
If religious institutions that make up doctrine some hundreds of years later claim that extra salvatory requirements are necessary for one to be saved, that is not written by any apostle, then it should be rejected. Therefore take all the alleged oral tradition and with a red pen cross out any doctrine that is not present in the writings of the first hand eye witness accounts such as ie purgatory, penance, salvation through relgious institution, forgiveness through relgious institution, Chief Priesthood outside of the non transferable Melchizedek of Christ, God the Father had sworn in their Chief Priest with an oath equal to Christ, religious institution is the way, the truth and the life, reglious institution is guarantor of a better covenant, institution is sinless and infallible equal to Christ and the list goes on.
If you only understood what claims are made through oral tradition of men who have assumed endorsement and authority from the apostles, then we really have a completely different faith and relgious institution as compared to the 1st century Ekklesia/Church. The claim of succession to the original faith looks rather implausible as what was pure and original had been altered to suit the hierarchical structure and mechanisation of a legalistic institution that would encompass the globe and involve itself in political matters completely outside of the great commission and outside of what the apostles were involved in back in the 1st century.
As Jesus said you will know them by their works and since a relgious institution has been made an idol to look up to, as being infallible by those making such claim, then we have to look at the works and policies of the institution from a historical point of view and not blame the fallible men who through the institution's policies made horrendous crimes against humanity and all in the name of religion.
I am sure that the apostles administration had nothing to do with the relgious institution that has evolved today from its inception until now. We have a completely different entity as compared to the 1st century relgious institution that was headed by the disciples.