There are several responses to the cosmological argument. The late physicist Victor Stenger, in his book God:The Failed Hypothesis summarizes them.
To me, I've never understood why matter and energy couldn't have always existed. If you believe a supernatural creative entity always existed, why not photons and particles? You know there are several cyclic models of the universe, describing how an endless series of expansions and contractions could have occurred, each resulting in a universe with different properties. Invoking supernaturalism doesn't answer the question. It just raises the question of how the supernatural entity came to be. And even if you overlook that problem, there are issues of how it works, and what are the specific characteristics of the supernatural. Is it one entity or many entities? Maybe there is one such entity for every quark or quanta of energy in the universe. Why not?
Having established that the universe could not have created itself, we are either left with the universe existing eternally or it being the result of some cause which transcends it, i.e. a supernatural cause.
I've never understood why matter and energy couldn't have always existed.
The Second Law of Thermodynamics states, among other things, that the universe is running out of usable energy. With each passing moment, the amount of usable energy in the universe grows smaller, leading scientists to the obvious conclusion that one day all the energy will be gone and the universe will die. Like a running car, the universe will ultimately run out of gas.
If the universe has existed for all eternity, i.e. if matter and energy have always existed, the second law tells us that the universe would look quite different than the one we actually observe. It would be totally devoid of usable energy. There would be no stars for example. The fuel and energy in them would have been burned up. But when you walk outside, the warmth of the sun on your face testifies to you that it is giving off energy and that therefore, we are living in a universe which had a beginning at some point in the past.
If you believe a supernatural creative entity always existed, why not photons and particles?
This is a good question. The short answer would be simply that I have good evidence that a supernatural creative entity has always existed and I also have good evidence that photons and particles have not always existed.
You know there are several cyclic models of the universe, describing how an endless series of expansions and contractions could have occurred, each resulting in a universe with different properties.
Yes I am aware of the cyclic models. The standard model however is superior to them all because it is simply better evidenced. In fact there really is no comparing the cyclic models with the standard model, for there simply is no evidence whatsoever that there has been an endless series of expansions and contractions of the universe.
Invoking supernaturalism doesn't answer the question.
That all depends on what question you are referring to.
It just raises the question of how the supernatural entity came to be.
Something exists necessarily, i.e. by virtue of its nature, it could not cease to exist and is not dependent upon anything else outside of itself for its existence.
Either the universe exists necessarily or something beyond and transcendent over the universe exists necessarily.
It is either or. If the universe does not exist necessarily, which as I have argued it does not, then there exists a necessarily existing supernatural cause of the universe and since this cause is necessarily existing, i.e. has always existed, then the question of how this being came to be is answered. The problem evaporates! This cause exists necessarily. It never came to be and will never cease to be.
With regards to your specific questions about the nature of this supernatural entity, that is a theological issue.
My main goal here is to get you to the point where you are comfortable with acknowledging that indeed there is good evidence that the supernatural exists. Specifics can come later.