Did the earliest information about Christianity circulate entirely in oral form?

A post I wrote last week about Josephus was partly about the likelihood that the earliest Jewish opponents of Christianity communicated about the religion in writing. Elsewhere in Tom Schmidt's book that I cited, he discussed a line of evidence I've brought up before. "For the same reason during the 30s CE it is probable that Saul of Tarsus received letters from none other than a high priestly son of Ananus I instructing him to arrest followers of Jesus." (Josephus And Jesus [New York, New York: Oxford University Press, 2025], 185) In a footnote, Schmidt cites Acts 9:1-2 and 22:5. There are other examples of actual or potential references to Christianity in written sources that are no longer extant, among both non-Christians and Christians. See my post here that discusses the example in Acts mentioned above and others. See, also, my discussion here regarding how the genealogy of Jesus in the gospel of Luke likely came from the brothers of Jesus, most likely James, and probably in written form.

What Justin Martyr said about early Jewish responses to Christianity, which I discussed in my last post, probably involved written material as well, not just oral sources.

People often speak of the earliest history of Christianity as if it involved only oral communication about the religion or as if any written sources that existed at the time had little or no significance. But that doesn't make much sense in the abstract, it's inconsistent with the large amount of documents we have from Christians from the middle of the first century onward, and it's contradicted by the references we have to early written sources that are no longer extant (the likely presence of written documents other than the canonical gospels in the "many" sources of Luke 1:1-3; Acts 9:1-2, 15:23-29; etc.). The nature of life is such that communicating orally makes more sense in some contexts, and communicating in writing makes more sense in other contexts. Both would have been present from the start of Christianity, not just later on. And that start of Christianity includes Jesus' life before his public ministry.