The argument of the existence of God from the First cause is one of the Five Ways from Saint Thomas Aquinas.
  1. There are events.
  2. Every event has a cause distinct from it
  3. Everything that we observe is an effect of some previous cause.
  4. Since there cannot be an infinite regress of events, there must be some Uncaused Cause.
  5. God exists.
First off, (V) does not logically follow from (IV). It is not a deductive consequence of (IV). It is quite possible for (V) to be false even if (IV) should happen to be true.

Why? God as defined by Saint Thomas Aquinas is the Christian God. This being is in addition to being the creator of the world is omnipotent, omniscient, and omnibenvolent. There is nothing in the argument that shows that these properties exist in the Uncaused Cause. Thus, the inference from a first cause to the existence of God is invalid.

Secondly, the Birthday Fallacy. (I) and (II) imply that there is at least one causal chain of events, and (III) tells us that all of them have a first member. This first member, cannot have a cause, otherwise it wouldn't be the first member of the chain. Thus each chain must have a first member. It does not follow that every causal chain must have the same first cause. This would be akin to claiming that everyone who has a birthday has the same birthday. (I) - (III) do not show that there is just one first cause.

Next, (I) - (III) are inconstant. These premises imply that every causal chain has an uncaused cause. This means that some event has no cause, which is in contradiction to (II). They cannot all be true.