No, it does not necessarily imply a point of origin. Maybe a three dimensional submanifold of origin.
Again, that sounds like a very strange usage. If a tree limb falls, that is not an accident. There is no intention either way.
I see the Big Bang as closer to the South Pole. It represents that time does not go farther back.
Fair enough. But then, why assume intention? It only makes the explanations more difficult.
The polar analogy works because it describes a point on the two dimensional boundary of a three dimensional object. The electro-magnetic field generated by the poles mostly exists beyond this boundary. And while there is no South of the South Pole on the two dimensional surface of the globe, space “below” the South Pole exists once we recognise an additional spatial dimension; so it may only be within the limitations of the four dimensional manifold we currently conceive of
, that space and time don’t extend beyond the limits of the universe (should we ever confirm what it’s temporal limits are).
As for accident vs intent, we know that the effect of a limb falling from the tree has a cause (or web of causation). So ‘intent’ in the context of the origin of the universe, is a question of first causes. An ‘accidental’ Big Bang is one in which the low entropy specialness of the early universe would have to have occurred randomly, and while only “back of the envelope” efforts - by Penrose for example - can be undertaken to calculate the probability of that happening, it still seems an utterly insignificant probability. That’s one reason, I think, that some astronomers entertain various multi-verse hypotheses; because in the context of an infinity of universes, statistical near-impossibilities become not impossible but inevitable.
But really I accept that there are no strong arguments for God from physics. We are far more likely to apprehend God through poetry than through science; He communicates with us using the language of the heart, not the head. That said, there is a poetic beauty in what we can glimpse of the narrative of the universe; stellar nurseries, galaxies, black holes, supernovas - what a work of art they constitute. And where there is a work of art, there has to be an artist.