No. It's very much based in logic, despite whether you're able or willing to recognize the logic.
You took issue with the argument ex nihilo, claiming that it makes special pleading for God--i.e grants God an exception to the logic that is applied to the universe. However, the argument ex nihilo demands, by definition, some construct such as God that would be the uncaused cause. Ex Nihilo nihil fit. From nothing, nothing comes. i.e. If something exists, then some uncaused something by definition had to exist. It's built into the logic. It is not a special pleading.
The logic of the ex nihilo argument is sound and rooted in the most basic laws of logic that we have. As a matter of fact, without the laws of causation, rationality and logic would cease to exist.
The basis of such laws, and the ex nihilo argument, is that every effect must have a sufficient cause.
That's the most basic. Ripples in a pond were caused by something. And a tsunami wasn't caused by a frog jumping into the ocean.
Now, if the universe is an effect (if it had a beginning), then the universe must, by the laws of causation, have a sufficient cause.
All indications are that the universe had a beginning. Science has pointed us to the singularity of the beginning of the universe. Logic tells us that an infinite regression of moments is a logical impossibility.
Science goes further to tie time and matter together inseparably. It shows that when the universe began, time began as well.
In case it's not obvious, the laws of causation that the ex nihilo argument are based on, are dependent on the existence of time, for the description and observation of causes/effects are at base a description of change over time. An effect comes after a cause, by definition.
So... The universe had a beginning, making it an effect. All effects must have a sufficient cause, therefore the universe must have had a sufficient cause.
That cause must be external to the universe and not bound by the universe, so it is outside of both matter and space.
Outside of--and unbound by--time, it is therefore not subject to cause and effect, and is eternal.
So, if that cause is God, God would be eternal and uncaused.
As I tried to point out earlier, and you were either unable or unwilling to grasp, you are making a classification fallacy.
And as I mentioned, all you have to do is change its class/type of the universe and it will have the same insulation of the ex nihilo argument that God would.
It is not special pleading. Now, it's up to you to either grasp that, or not. Whether you do has no effect on the veracity of the argument.