1. The existence of an effect which requires the operation of a co-existent cause implies the co-existence of that cause.
  2. Whatever exists either does, or does not, need a cause of its existence at every moment of its existence.
  3. A contingent being is one that needs a cause of its continuing existence at every moment of its existence.
  4. No contingent being causes the existence of any other contingent being.
  5. Contingent beings exist in this world and endure in a temporal frame, with a beginning and an end.
The (faulty) conclusion is that there exists a cause of the existence of contingent beings, namely a supreme being, which might commonly be referred to as "God". Why is that faulty?
Premises 1, 2, and 5 are either self-evident, or true beyond a reasonable doubt. Premise 4 seems to accord well with common sense and empirical observation. The problem premise is 3, which asserts without basis that we contingent beings depend on a cause for our continued existence. In physics, we observe the principle of inertia: objects in motion tend to stay in motion, and objects at rest tend to remain at rest, until acted on by external forces. It's not hard to imagine a similar principle of "existential inertia", whereby an object in existence tends to stay in existence, until some outside force interferes with its existence.