Even if I would agree with everything, the argument says nothing about the possibility of more causes not just one, why does it necessarily have to be only one uncaused cause and not many uncaused causes, we also don't know what that uncaused cause or causes are, you are just assuming it's god because you are religious.
We know that wherever is outside of the universe must logically be boundless, immaterial, indivisible and an uncaused cause. This is not an assumption but a logical necessity if the universe is finite and rational.
Is it rational to infer that this uncaused cause is God?
Well let compare what we derive by logical and mathematical necessity above to what Ethical Monotheism tells us about the nature of God.
The Nature of Godhttp://www.jewfaq.org/g-d.htmGod is One
God is a unity. He is a single, whole, complete indivisible entity. He cannot be divided into parts or described by attributes. Any attempt to ascribe attributes to God is merely man's imperfect attempt to understand the infinite.
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God is Incorporeal
God has no body. Any reference to God's body is simply a figure of speech, a means of making God's actions more comprehensible to beings living in a material world.
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God is Omnipresent
God is in all places at all times. He fills the universe and exceeds its scope.
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God is Eternal
God transcends time. He has no beginning and no end.
Note the symmetry between what logically must exist beyond the bounds of the universe and what religious tradition teaches.
''We know that wherever is outside of the universe must logically be boundless, immaterial, indivisible and an uncaused cause.'' Even if we agree with that and we shouldn't, the argument says nothing against a lot of uncaused causes, if everything that's outside the universe must have no cause then it could easily mean there are a ton of uncaused things outside the universe which doesn't solve any problem.