Was the first church the true church, and did it "fall" later?

Hegesippus (as Eusebius reports) c. 110–c. 180 ADMemoirs, in Eusebius, Church History 3.32.7–8

... that until those times the Church remained a pure and uncorrupted virgin, while those who tried to corrupt the sound rule of the saving preaching, if there were any, still lurked in hidden darkness. But when the sacred band of the apostles had reached the end of life in various ways, and the generation of those who had heard the divine wisdom with their own ears had passed, then godless error began to take shape through the deceit of false teachers.

Hegesippus sees heresies rising outside the Church after the apostles, not the Church itself falling.

Irenaeus of Lyons c. 130–c. 202 ADAgainst Heresies 3.4.1

What if the apostles had not even left us Scriptures? Would we not have had to follow the order of the tradition they handed on to those to whom they entrusted the churches? Many barbarian peoples who believe in Christ assent to this order. They have salvation written in their hearts by the Spirit without paper or ink, and carefully keep the ancient tradition, believing in one God, maker of heaven and earth.

For Irenaeus the apostles' teaching was never lost and never needed restoring: it was handed on publicly to the churches they founded and kept there, so that even peoples who had no writings held it whole. The passage survives in the ancient Latin translation; the Greek of Book 3 is lost here.

Tertullian c. 155–c. 220 ADPrescription against Heretics 28.1–3

Suppose, then, that all have erred; that the apostle was mistaken in giving his testimony; that the Holy Spirit took care of no church to lead it into truth ... Is it likely that so many churches, and such great ones, should have strayed into one and the same faith? Among many, chance never comes out the same. The error of the churches' teaching would have produced different results. But what is found to be one among many is not error but tradition.

Tertullian's argument against the claim that the Church had lost the truth.

Westminster AssemblyWestminster Confession of Faith 25.5

The purest churches under heaven are subject both to mixture and error; and some have so degenerated, as to become no churches of Christ, but synagogues of Satan. Nevertheless, there shall be always a church on earth, to worship God according to his will.

The Reformers held that the Church never vanished but had grown corrupt and needed reform.

Joseph SmithHistory 1:19

I was answered that I must join none of them ... were all wrong ... abomination in his sight ... were all corrupt

Smith's account of his 1820 vision, written in 1838 and first printed here; it is the founding Latter-day Saint claim of a general apostasy. The 1842 printing survives in a rough scan with interleaved columns, so the quotation is given in the cleanest verified spans.