It has been pointed out that premise 1 commits a fallacy of composition. That is, assuming the whole (the Universe) must also display features which are reasonably attributed to the parts. Namely, the property of having a cause.
The argument is made for an uncaused cause at best; however this "monadic" being need not look anything like a deity whose attributes are intelligence, purposefulness and everything else that might resemble a human-like God. In other words, cosmological arguments jump from a trivial metaphysical intuition to an unjustified anthropocentric, theological claim. As an example of alternatives to God which would also benefit from cosmological arguments, cosmologist Max Tegmark hypothesises that ultimate reality may be just a "Mathematical Universe" made of all logically necessary facts.
Similarly, it doesn't follow from accepting the conclusion (the Universe has a cause) that this cause itself was not in turn caused by something else.
According to cosmologist Sean Carroll, the premises are an oversimplification of our current state of knowledge in physics, and a misuse of the same thereafter. There is room for naturalistic explanations to the Big Bang. Strictly speaking, Big Bang theory doesn't claim the Universe began to exist in the 'ex nihilo' sense that is required by Abrahamic religions. Determining what caused it to expand from a very condensed state is a major open problem in cosmology.