The lack of evidence of early Christianity has been noted by many scholars.
Edward Gibbon, in The History of the Decline and Fall of the Roman Empire, said :"The scanty and suspicious materials of ecclesiastical history seldom enable us to dispel the dark cloud that hangs over the first age of the church.".
William Fitzgerald, in Lectures on Ecclesiastical History said: "Over this period of transition, which immediately succeeds upon the era properly called apostolic, great obscurity hangs ...".
Samuel G. Green in A Handbook of Church History said: "The thirty years which followed the close of the New Testament Canon and the destruction of Jerusalem are in truth the most obscure in the history of the Church. When we emerge in the second century we are, to a great extent, in a changed world.".
William J. McGlothlin, in The Course of Christian History said: "But Christianity itself had been in [the] process of transformation as it progressed and at the close of the period was in many respects quite different from the apostolic Christianity.".
Jesse Lyman Hurlbut, in _Story of the Christian Church, said:"For fifty years after Paul’s life, a curtain hangs over the Church, through which we vainly strive to look; and when at last it rises, about 129 A.D. with the writings of the earliest Church Fathers, we find a Church in many ways very different from that in the days of Peter and Paul.".
Other historians make similar comments about the lack of historical material from that period, and how, after a few centuries, suddenly Christianity is seen to be flourishing, with no evidence of how it got that way.
Whatever happened, it wasn't a smooth transition.
It's beyond the AD 70-220 range of this question, but the Council of Nicaea provides a good idea of what the process must have been like.
Describing the period immediately after the Council, historian Will Durant wrote, "Probably more Christians were slaughtered by Christians in these two years (342-3) than by all the persecutions of Christians by pagans in the history of Rome" (The Story of Civilization).
The Holy Roman Empire's version of Christianity was very different from the original Christianity spread by the Apostles. Once "Christianity" became the official religion of Rome, anyone practising anything resembling original Christianity was called a Judaizer and persecuted as a heretic.
It's hardly surprising that under such circumstances, any historical records that contradicted the new official version would have been suppressed and destroyed.
EDIT: as requested, here is some support of the Church's history of persecuting anyone that Judaizes.
From their very beginning, Christians were persecuted by Rome.
They were seen as nothing more than a sect of Judaism, and a troublesome one at that.
Norbert Brox, in A Concise History of the Early Church stated:
… the first [Christian] communities were groups that formed within Judaism … Christians believed as before in the God of Israel: their Bible was the Bible of the Jews … They continued to observe (as Jesus did) the Jewish practice of temple worship and law (Acts 2.46; 10.14), and gave outsiders the impression of being a Jewish sect (Acts 24:5; Acts 24:14; Acts 28:22), not a new religion. They themselves probably also simply thought of themselves as Jews
The destruction of the Temple and the extradition of Jews meant that the central body of the Christian Church could no longer exist in Jerusalem.
The Jewish Christians in Palestine had been driven out in the First Jewish War (66-70) but then had returned to Jerusalem; however, after the Bar Kokhba revolt, the Second Jewish War against the Romans (132-135), they had to leave the land because, as Jews, they had been circumcised, and all Jews were now banned on pain of death. So for the moment that meant the end of this [Jerusalem] church.
Christianity spread throughout the Empire, both by deliberate evangelism and by the dispersal of the Jews.
The Church thought of itself as a continuation of Judaism, and gentile converts became spiritual Israelites, accepting the teachings and practices of the Holy Scriptures.
Iranaeus, circa 190, convinced Pope Victor I not to excommunicate Christian communities that celebrated Passover rather than Easter.
Eusebius wrote of Polycrates of Ephesus (AD 130-196):
A question of no small importance arose at that time. For the parishes of all Asia, as from an older tradition, held that the fourteenth day of the moon, on which day the Jews were commanded to sacrifice the lamb, should be observed as the feast of the Saviour's passover … But it was not the custom of the churches in the rest of the world … But the bishops of Asia, led by Polycrates, decided to hold to the old custom handed down to them.
He records Polycrates' letter to the Roman church:
We observe the exact day; neither adding, nor taking away. … [list of saints, including John and John's follower Polycarp] All these observed the fourteenth day of the passover according to the Gospel, deviating in no respect, but following the rule of faith. And I also, Polycrates, the least of you all, do according to the tradition of my relatives, some of whom I have closely followed. For seven of my relatives were bishops; and I am the eighth. And my relatives always observed the day when the people put away the leaven. I, therefore, brethren, who have lived sixty-five years in the Lord, and have met with the brethren throughout the world, and have gone through every Holy Scripture, am not affrighted by terrifying words. For those greater than I have said 'We ought to obey God rather than man' … I could mention the bishops who were present, whom I summoned at your desire; whose names, should I write them, would constitute a great multitude. And they, beholding my littleness, gave their consent to the letter, knowing that I did not bear my gray hairs in vain, but had always governed my life by the Lord Jesus.
The following examples extend well beyond the question's AD 70-220 range, but they provide evidence of the continued persecution of anyone considered Judaizing. It's not difficult to extrapolate this evidence back to a time when the suppression of the practices of the original apostolic church were so severe that they destroyed not only the practice but the evidence of such practice.
When Emperor Constantine decided to incorporate rather than fight the Christian sect, he ran into a problem.
Much of Christianity still considered itself to be part of the same religion as the Jews, and so was very resistant to the changes that Constantine wanted to make.
This situation came to a head when it came to replacing the biblical Passover celebration with the Roman Easter.
Many leaders of the Christian Church welcomed this change, as it would provide a more familiar event for their members, and would attract more converts.
But those leaders that saw themselves, and Christianity, as a more enlightened form of Judaism strongly opposed it.
Constantine used anti-Semitism to silence, and eventually ban, the descenting Christian leaders.
In a letter talking about Jewish Christians, quoted by Eusebius of Caesarea, Constantine wrote:
And truly, in the first place, it seemed to everyone a most unworthy thing that we should follow the custom of the Jews in the celebration of this most holy solemnity, who, polluted wretches!, having stained their hands with a nefarious crime, are justly blinded in their minds.
It is fit, therefore, that, rejecting the practice of this people, we should perpetuate to all future ages the celebration of this rite in a more legitimate order … Let us then have nothing in common with the most hostile rabble of the Jews.
We have received another method from the Savior. A more lawful and proper course is open to our most holy religion … Let us withdraw ourselves, my much honored brethren, from that most odious fellowship
When Constantine convened the Council of Nicaea, he made sure that no Judaizers, members of Christian communities that practised traditional Passover, were invited.
But even with a stacked deck, the banning of Passover wasn't unanimous.
Constantine easily resolved that issue too. Historian Robin Lane Fox speaks of Constantine in Pagans and Christians:
At Nicaea, the Emperor himself imposed criminal sentences of exile on the bishops who refused to sign. He also investigated other reports of heresy
This suppression and persecution of Christians that insisted on following the traditions and practices of Jesus and the Apostles continued.
Following the adoption of the Trinity doctrine, for instance, Emperor Theodoseus declared:
We authorize the followers of this law to assume the title of Catholic Christians; but as for the others, since, in our judgement, they are foolish madmen, we decree that they shall be branded with the ignominious name of heretics, and shall not presume to give their conventicles the name of churches.
In 431, Pope Celestine sent Palladius to convert Ireland. There he encountered existing groups that claimed their Christianity was directly descended from the Apostles. The Catholic Encyclopedia records that:
those fierce and cruel men [did not] receive his doctrine readily.
In 595, Pope Gregory I sent Augustine, first Archbishop of Canterbury, to convert Britain.
He was successful in the eastern parts, which had a long history with the Roman Empire, but in western Britain he encountered a version of Christianity that had been founded by missionaries from Ireland centuries before. These "heretics" still celebrated Passover.
The Paulician church of Armenia rejected the power of the Church, including mass, communion, and confession. They saw the worship of Mary, the concept of Trinity, Sunday worship, Christmas, and Easter all as paganism, added by Rome. F.C. Coneybeare wrote: "we have before us a form of Church not very remote from the primitive Jewish Christianity of Palestine". In 843, Empress Theodora persecuted the Paulicians, murdering 100,000 and confiscating land and property.
Similarly, groups such as Bogomils, Waldensians, and Cathars, who followed biblical teachings rather than the traditions of Rome were persecuted and slaughtered.
The Roman Church continued its suppression of anything resembling Judaism within Christianity right through the Reformation.