Here are common misconceptions about Aristotle's proof for the existence of God, based on the fact that motion exists.
Misconception 1: The Big Bang theory completely discredits this proof.
We can confidently say that the Big Bang is the source of all motion in the known universe. However, Aristotle's questions about motion still apply here. Namely, what set the Big Bang in motion?
Modern science has no definitive answer to that question. Therefore, Aristotle would continue to conclude that there must be an immobile mover responsible for movement.
Misconception 2: Aristotle proved the existence of a creator god.
No, Aristotle proves the existence of a god, who is the source of all movement. Aristotle did not believe in a creator god, because he though the world exists forever. Those two notions of God were separate in Aristotle's mind.
As a side note, when St. Paul preached in Athens (the town where Aristotle lived for many years), he made the connection between "God as creator" and "God as source of all movement". Specifically, he said, "The God who made the world and all that is in it...gives to everyone life and breath and everything...In him we live and we move and we have our being" (Acts 17:24-8, emphasis mine).
Misconception 3: The primary mover only caused movement once.
Aristotle's proof shows that there is a god, who is the source of all movement. This god is responsible for the first movement, ever. However, Aristotle did not believe this was a one-time thing. He believed that this god continues to create movement, while remaining unmoved.
Aristotle theorized that each planet has its own unmoved-mover god, who makes the planet move. In part, this is why all the planets in our solar system are named after Greek gods.