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It would be, if English had a more rigid word order. Or in written English, where the stresses and intonation of the spoken language do not always translate well, even when typographical cues like italics are employed.

In the case where one is stating that God merely knows, there would be a subtle stress and (usually) a rise in intonation over the word only (which would be more pronounced if one were being explicit, as when countering a suggestion that God should have been able to do something about the situation).

Without the stress (or with the stress on God instead), the two formulations are equivalent in meaning. Well, sort of equivalent. God only knows is an idiomatic phrase meaning more-or-less I don't know, and I doubt that anyone else does either. The alternative, Only God knows, is a little more philosophical, theological, or at least religious in tone, and means something more along the lines of That's beyond the ken of mere mortals. The strict literal meanings of both formulations are the same, but the implications are different because the more archaic inverted version has become idiomatic and lost its theological implication. An Anglophone atheist would have no more trouble saying God only knows in an ordinary conversation than, say, God damn it, but would only use Only God knows ironically.

For a specific object, use past tense because we are talking about its history, but for something representative of a class (like milk in general) use the present tense since the same answer applies to all instances. The first is about an object having arrived from somewhere else, the second is about the origins of that thing in general. So, that bottle of milk came from the supermarket, but milk in general comes from cows or similar arrangements thereto.