Blanket statements are great for keeping warm at night, but one has to be careful when they get too large because there will always be great holes near the edges.
Exegesis involves supporting any assertions with specific scriptures, context, linguistic analysis, cultural context, historical manuscripts or references, archaeological findings, opinions of experts, and logic to build a case. In many situations, one is dealing with likelihoods. So, when reading letters in the New Testament, one often needs to extrapolate the other, unrecorded half of the written conversation to help with the interpretation.
For example, Didache, The Lord's Teaching Through the Twelve Apostles to the Nations, was likely first written near the end of the first century, likely after the New Testament books were available. Nevertheless, even though it’s not considered inspired scripture, exegetical support can be derived from this later text regarding many types of support listed above in exegesis—if for nothing else, as a snapshot in time for how early Christians interpreted the New Testament.
In any case, one has to be very careful in applying extra-biblical information, understanding its limitations. This also applies to hostile testimonies recorded around that time.
For example, the famous Alexamenos graffito depicting the crucified Christ with a donkey's head is dated to between the late first and mid-third centuries CE according to the Biblical Archaeology Society. This image captures quite a bit of information about early Christian beliefs from a hostile witness and it is considered the earliest depiction of the crucifixion of Christ.