1. Whatever is changing has an external cause. (Premise)
2. The universe as a whole is changing. (Premise)
3. Therefore, the universe as a whole has an external cause. (Premise)
The argument is logically valid, so what about the truth of its premises?
I defend premise (1) with two distinct arguments - one deductive and one inductive. First, whatever is changing exhibits actuality (its current existence and state of being) and potentiality (what the thing could be). Now, no potentiality can actualize itself. Otherwise, the thing would be self-caused, and exist and not-exist simultaneously in order to cause its own actualization. This is a contradiction.
Secondly, an acorn, for example, cannot continue becoming an oak tree unless there are external causes, such as water, sunlight and soil. If at any point these external causes are removed, then the acorn will cease its change, whither and die.
But why does the cause have to be external? Quantum fluctuations have at the very least material causes, which are internal within the quantum vacuum. The problem with this objection is that the fundamental forces of nature - gravity, electromagnetism, and the strong and weak atomic forces - all exist as external causes of the allegedly externally uncaused changes. Premise (1), therefore, is correct.
As for premise (2), the most common objection is that the premise commits a composition fallacy. Just because every part of a mountain is small doesn't mean the mountain as a whole is small. However, there are just as many instances in which the whole is like its parts. If every part of a mountain is made of rock, then the mountain as a whole must be made of rock. Moreover, the mountain as a whole is externally caused by the forces of nature and various geological processes. Now, if every part of the universe is changing, then the universe as a whole must be changing. Hence, premise (2) does not commit a composition fallacy and is also correct.
Given the truth of (1) and (2), it necessarily follows that the universe has an external cause. Since the universe is the sum total of all physical space, time, matter and energy, the external cause of the universe must be timeless, changeless (for time is a measurement of change) and immaterial, in addition to being very powerful in order to externally cause the change of something as vast as the universe.
Whether you want to call this external cause "God" or not is inconsequential. The argument, if sound, is certainly a defeater of Naturalism. Call it the universe's First Cause if you'd like.