No. That would be a waste of the paper and make it too specific. God is just one of countless absolutes. Others include infinity, eternity, perfection, truth, certainty, and teenage love, LOL, etc.
There are no proofs for or against the existence of God. But to raise that as part of your argument would show that you are confusing an attempt to argue against absolutes with the attempt to refute ONE example of a supposed absolute, and you cannot prove a rule by one example or by an exception.
One argument you can use is to point out that no objective absolutes exist in our universe that you can point to and say that "there is an absolute" like you could with a flower or pony.
You have to also refute the argument that there are absolutes in this universe in the forms of mathematical absolutes and in physics you have absolute zero temperature.
You refute the first by saying that mathematics is the result of following coherent and consistent rules that always produce the same results. Nothing absolute there. The confusion is between consistence and absoluteness.
Absolute zero temperature is absolute in name only. Nothing absolute about nearly motionless molecules and atoms.
Another way to argue against absolute truth is that that would imply complete certainty. We don't have complete certainty in this world but only a probabilistic certainty. You might believe or assume that something will turn out a particular way, you may feel certain, but that doesn't mean it will turn out that way. People have been absolutely certain about all sorts of things that turned out to be false. While a truth table can show truth for complex statements, it is not showing "absolute truth", especially not in a religious sense.
In summary, argue against the concept of absolute instead of any few examples of absolutes. Try to be sensitive to the fact that different people use the term absolute in different ways, so start by defining what is meant philosophically by the term absolute. For example, the person posting immediately after me is confusing absolute with sensorial knowledge. All knowledge including moral knowledge is conditonal which means it is not absolute. So it is easy to get confused.