Two questions about how central the question of origins is to your core beliefs

No.

Such is not one of the reasons why I believe.

Perhaps the most helpful would be reason #2 in this link, where I might say that existence of some ideas of a Creator would support the faith that life is worth living.

The only meaningful task I can see for apologetics is to defend the rationality Christianity, which would not preclude the rationality of alternatives. It would only consist of logical coherence, consistency with the objective (scientific) evidence, and compatibility with the ideals of a free society. These would simply exclude understandings of Christianity which failed these criterion.

But I guess you are referring to the more traditional idea of concocting one of these proofs/arguments for the existence of God – something which I routinely oppose. That is because this sort of thing would amount to an argument that any alternative would not be rational.

I can’t conceive of why I would want to do that.

It has been my often stated position that the ends are not independent of the means. In particular, life cannot be created instantaneously. Thus the creation of life really began 13.7 billion years ago with the creation of universe. Thus that is where begins this role I see for God of supporting the faith that life is worth living. He is a parent not by accident but by intention. Can’t you see how this contributes to a faith that life is worth living?

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