Question: Is there any Biblical evidence that the apostasy began?

The apostasy was foretold, and the apostles struggled against it for their whole careers

The Bible predicts an apostasy from the church founded by Jesus Christ. Is there any Biblical evidence that this apostasy began?

The apostasy was foretold, and the apostles struggled against it for their whole careers. Threats came from within and without the Church. Members lusting for power would not recognize those with authority. Much of our New Testament is a witness to the fact that the churches would deviate from the truth without apostolic guidance: if everything was moving along fine, why does Paul (for example) spend so much time answering questions, correcting errors in doctrine, and trying to persuade people to change how they are running the Church?

One must remember, the letters aren't to the unbelievers—they are addressed to erring Christians!

The Greek word translated as "apostasy" (αποστασία) meaning a defection or revolt, from απο, apo, "away, apart", στασις, stasis, "standing". Thus, an "apostasy" is not a failure of the Church due to persecution from without, but is fundamentally about the betrayal of the Church and the apostles from within.

In Revelation, the Lord speaks through John to one of the Christian churches, and commends them for avoiding those who claimed (falsely) to be apostles having authority from him. However, he also says that the Church has still fallen into some errors, and must repent:

2 I know thy works, and thy labour, and thy patience, and how thou canst not bear them which are evil: and thou hast tried them which say they are apostles, and are not, and hast found them liars:
3 And hast borne, and hast patience, and for my name's sake hast laboured, and hast not fainted.
4 Nevertheless I have somewhat against thee, because thou hast left thy first love.
5 Remember therefore from whence thou art fallen, and repent, and do the first works; or else I will come unto thee quickly, and will remove thy candlestick out of his place, except thou repent. (Revelation 2:2-5)

Many of the letters of the New Testament were written to correct errors that had crept in among the members

Much of the New Testament is composed of letters from apostles to the Church. Many of these letters were written to correct errors that had crept in among the members. If this was happening while the apostles were alive, how much worse must it have been when they had all been killed? Paul writes to one congregation:

6 I marvel that ye are so soon removed from him that called you into the grace of Christ unto another gospel:
7 Which is not another; but there be some that trouble you, and would pervert the gospel of Christ. (Galatians 1:6-7)

In Second Corinthians, Paul likewise warned of false teachers among the Christian churches:

13 For such are false apostles, deceitful workers, transforming themselves into the apostles of Christ.
14 And no marvel; for Satan himself is transformed into an angel of light.
15 Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works. (2 Corinthians 11:13-15)

Even in New Testament times, the apostles were being opposed by some members of the Church

Even in New Testament times, the apostles were being opposed by some members of the Church, some of whom were "false apostles." The apostasy (or "mutiny") had already begun. John writes about one Church member who wanted to be a leader, would not receive letters from the apostles, would not receive those with authority into the Church, criticized the apostles, and threw out the members who wanted to receive those with authority:

9 I wrote unto the church: but Diotrephes, who loveth to have the preeminence among them, receiveth us not.
10 Wherefore, if I come, I will remember his deeds which he doeth, prating against us with malicious words: and not content therewith, neither doth he himself receive the brethren, and forbiddeth them that would, and casteth them out of the church. (3 Jn 1꞉9-10
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One can see how, with the apostles gone, it would have been almost inevitable that people seeking for glory and power within the Church would take over, and change the doctrines, teachings, and practices to suit themselves. It was already happening when the apostles were alive!

At the end of Paul's life and mission, he noted that all those whom he had taught in Asia had turned away from what he had taught

At the end of Paul's life and mission, he noted that all those whom he had taught in Asia had turned away from what he had taught. Again, if this was happening while the apostles were still alive to try and correct people by letter, what would happen when the apostles were dead?

13 Hold fast the form of sound words, which thou hast heard of me, in faith and love which is in Christ Jesus.
14 That good thing which was committed unto thee keep by the Holy Ghost which dwelleth in us.
15 This thou knowest, that all they which are in Asia be turned away from me; of whom are Phygellus and Hermogenes. (2 Timothy 1꞉13-15
(emphasis added)

Notes

Question: Is there any Biblical evidence that the apostasy began?