One distinctive feature of Mormons is the belief that there were Christians before the incarnation of Christ - this is documented (in two different groups) in the Americas in the Book of Mormon.
These were Christians who knew by personal revelation and prophecy that a savour and redeemer, Christ, would come - and that his atonement would potentially cover everybody - before, during and after His incarnation - and who therefore practised a Christ-centred religion even before Jesus was born or resurrected.
I believe in the truth of the BoM; but even for a Christian who did not, there is a real possibility that what it describes specifically may have happened in one or more places.
How might Christians have existed before Christ?
My hunch is that a Saviour is something that would make sense only to those who were, in some sense, monotheists - those who believed in One God.
(Not necessarily a belief in a one-and-only God but a supreme, authoritative and ruling personal God who had a care for Men - individually and collectively.)
It is not that a Saviour is unnecessary in a polytheistic system, but rather that there is (apparently) a considerable muddle and imprecision about polytheism, such that its philosophical implications(including deficiencies) are unclear, and undiscussed.
How might Christians before Christ know about Christ? Here are three possible lines of evidence.
1. Revelation - personal revelations to individuals, and to acknowledged prophets, may have been made by God to communicate the need for a Saviour, and the promise of a Saviour.
(God might make such revelations open to all Men and all societies; but they may not be looked for, or may be ignored or rejected.)
2. Reason may have worked-out the need for a Saviour; individuals may have understood that pure monotheism was philosophically-inadequate (even in principle) to provide and account for the combination of factors which characterised the human condition in relation to the divine.
(This argument is based on the fact that Christianity offers, or promises, more than any other religion - as was recognized by Blaise Pascal; in other words, other religions have more gaps and deficiencies.)
3. Psychology - people may have felt the need for a Saviour; may have recognized that they could not save themselves, and that for them to be saved required some kind of mediator between God the Father and man.
And they may have felt that because they personally needed a Saviour, then a loving God of power would 'provide' a Saviour.
(This is another place where it seems that monotheism is required to understand the necessity of Christ - those who believe in a polytheistic pantheon do not regard them as responsive to human needs.)
So, it is possible that early men may, for a variety of reasons, have concluded that Man required a Saviour; and that what Man needed God would somehow give.
Also that because a Saviour is once-and-for-all, it did not much matter whether He had not yet come: life should still be lived with that awareness.
And so some early men may have practised de facto Christianity.
My favourite is the Neolithic inhabitants of England who built the Avebury, Silbury, Stonehenge and the other linked outdoor temples, stone monuments, pathways and spaces across southern England.
I like to speculate, to imagine, that these people were monotheists - with their supreme sky God-the-Father associated with the sun - and that they were awaiting some intermediary Saviour who was Son to the Father God.
This is compatible with what little is known of these societies; but there is no positive evidence that I know of - indeed I do not know what might count as positive evidence of a proto-Christian religion among the kind of things that survive to be noted by archaeologists.
Only if some kind of writing is found from this era, and is deciphered, could we perhaps really know. But if archaeologists aren't even looking for proto-Christianity or rule-it-out a priori (because, as typical secular modern people, the idea strikes them as absurd) then of course they never will find it.