Why is there no archaeological evidence that Christians existed for 200 years after 70 AD? This is from the 2/1/2018 issue of Biblical Archaeology Society:

...For almost two hundred years after the crucifixion, Roman cities are entirely devoid of any trace of early Christians; to date, no one has ever found any object that’s been plausibly connected to them. As an archaeologist and a historian, I think it’s time we start taking this silence seriously and stop trying to fill it with any more sensational “discoveries.” Many of Jesus’ followers—men and women who lived in the first, second and even third century Roman Mediterranean—simply didn’t want to be found.
That’s not exactly the first thing that usually comes to mind when we think about early Christians, but the evidence is insurmountable at this point. For almost four hundred years, there were no manger scenes anywhere in the Roman world. There were no crucifixes displayed in homes or schools. There weren’t even any bound Bibles tucked into church pews. In fact, we actually don’t even know what “churches” looked like, at least, not until the middle of the third century. For a community that would later come to remember its earliest history as a time of vicious persecution, answered with outspoken acts of martyrdom, this archaeological silence poses a slight problem. Where are these people?...
Here are some standard evidences of the early existence of Christianity:


Many extant Bible MSS date from before 350 AD such as p1 (3rd), p4 (3rd), p5 (3rd), p9 (3rd), p15 (3rd), p20 (3rd), p52 (about 125), p90  (2nd), p98 (2nd), p104 (2nd), and many more). There are also many important archaeological artifacts.  (See a more complete list of MSS in UBS4, UBS5 NA27, NA28.)
The voluminous writings of all the ante-Nicaean Fathers (e.g., Ignatius, Clement, Polycarp, Justin Martyr, Tertullian, and Origen), starting at about 110 AD.  (My sets consist of The Apostolic Fathers by Holmes [Baker Academic] and Ante-Nicene Fathers [T&amp;T Clark Edinburgh, Eerdmans Publishing])
The writings of Josephus (about 90 AD) refer to Christians, Christian practice, Christian belief, and even Jesus. 
Chapel of Saint Ananias, Damascus, Syria, dates from the first century.
A fragment of an inscription bearing the name of Pliny, Basilica of Sant'Ambrogio, Milan.  Pliny the Younger, the Roman governor of Bithynia and Pontus (northern modern Turkey), wrote a letter to Emperor Trajan around 112 AD and asked for counsel on dealing with Christians. The letter (Epistulae X.96) details an account of how Pliny conducted trials of suspected Christians who appeared before him as a result of anonymous accusations, and in the letter he asks for the Emperor's guidance on how the the Christians should be treated. 
Tacitus (a Roman senator) wrote in his book (circa 116 AD) about Jesus and His execution under Pilate, and the existence of Christians in Rome ("Annals" book 15, chapter 44). 
The Roman historian Suetonius (c. 69 – after 122 CE) made references to early Christians and their leader in his work Lives of the Twelve Caesars (ca. 121 CE). The references appear in Claudius 25 and Nero 16, and they describe the lives of Roman Emperors Claudius and Nero.
Documents excavated at Oxyrhynchus show many writings about Christianity dating from the first- and early second century.
ΙΧΘΥΣ (Ichthys--fish inscriptions dating from the second century.
Numerous Christian graves in the Catacombs of Rome dating from the second century.


There is much more, and all of it well known.

We should not be surprised we have as much as we do to document early Christianity.  Up until Constantine issued the Edict of Toleration from Milan in 313, which legalized Christianity, Christianity was illegal and suffered numerous purges and persecutions, culminating with Diocletian's attempt to annihilate Christians. However, much evidence has survived, as I've documented above.

See also A History of Christianity Regions 2 &amp; 4 (DVD) for more general information about early Christianity.