I’m going to say, overall, that the answer is ‘no’, in that ‘Oral Tradition’ isn’t a solution to asking where the doctrine of the Trinity arises in early Christianity.

It’s going to take a bit of conceptual work to establish why I think this is the answer here.

1. The development of a doctrine of the Trinity is a development within Christian thought. It’s helpful here to realise what the area of theology called systematic theology is. It’s an attempt to answer the question, “What things must be the case, if the Christian faith and its scriptures are true?” That is, it’s an attempt to provide a systematic presentation of the underlying truths that must be the case if Christianity is true and if the statements within Christian scriptures are true.

Why is this important? Because obviously the Bible is not a collection of systematic propositions. That’s why it doesn’t contain any particular formulation of the Trinity. It would be anachronistic to look for, say, 4th century type formulations of Trinity in 1st century documents like the New Testament corpus.

So, when we do read Christian authors of the 2nd through 4th centuries talking about Trinity, they are trying to make sense, and often argue polemically, about what to do with the ‘facts as they understand them’ or the given data of the Bible.

2. There are different scholarly positions on how to characterise devotion to Jesus in earliest (1st century) Christianity. I’m persuaded by authors like Richard Bauckham and Larry Hurtado that there was, from the earliest stages, a fairly unique combination of factors that show that Christians treated Jesus as being in the identity of the One God of Israel. I’d call this binitarianism, and argue that it’s explicit in the New Testament corpus but in practice, not explained theoretically.

3. There is a form of (oral) tradition that appears in 2nd-4th century documents, the Regular Fidei or Rule of Faith. It appears most often as an appeal to teaching ‘universally held’ by the churches in every place and associated partly with the emergence of a monarchic episcopacy (that is, a singular bishop in an authority relationship over presbyters, usually in a city context). However it’s not really possible to posit a kind of ‘this is oral tradition’ which contains a doctrine of Trinity, except to say that Christian communities treated Jesus as God even when they didn’t necessarily reflect on what it meant to treat Jesus as God.

4. The reason the 4th century is so important for this (and the reason why it’s my primary field of research) is that you get a lot of explicit discussion of the Trinity. By this stage there’s a fairly stable canon of scripture and treatment of that canon as authoritative. But at the start of the 4th century it’s like (as Anatolios puts it), there’s a fracture in the common experience of the collective church that causes a re-evaluation of what had been taken mostly for granted until then. This causes Christian thinkers to go hammer-and-tongs at working out ‘what has to be the case in order for this to work’.

5. The issue of the status of the Holy Spirit tends to only enter that 4th century debate in the latter half of the 4th century. The major debate was how to relate the Father and Son. The solution to this largely set the blueprint (for each party) for how to also understand the Spirit. This process more or less made explicit the implicitness of the binitarian formulation into an explicit trinitarianism.

Happy to cover follow-up questions on this or related areas.