The Cosmological Argument is the First Cause argument. Essentially:
1) Everything has to have a cause.
2) There must have been a first cause.
3) That first cause, we call God.
Setting aside the fact that, even granting all these premises, you can't then derive any information about that god from this argument, this argument is self-refuting.
Thomas Aquinas phrased this argument a few different ways and called them all different arguments. But, really, they're all just iterations of the Cosmological Argument.
Below, I'm posting a section of the Transcendental Argument for God from CARM.org, but not the entire thing because it's very lengthy.
Their own summary goes like this:
Logical absolutes exist. Logical absolutes are conceptual by nature, are not dependent on space, time, physical properties, or human nature. They are not the product of the physical universe (space, time, matter), because if the physical universe were to disappear, logical absolutes would still be true. Logical Absolutes are not the product of human minds, because human minds are different, not absolute. But, since logical absolutes are always true everywhere, and not dependent upon human minds, it must be an absolute transcendent mind that is authoring them. This mind is called God.
The first half can be summarized as, "Yes, if a tree falls in the woods and no one hears it, it does indeed make a sound." I agree with that. Sounds are not defined by whether or not they are heard, they are defined by sound waves. All our experience shows that a tree falling creates sound waves.
You might feel a bit of a logical hiccup once you get toward the end of this summary, though. There are a number of them, but this particular hiccup becomes more obvious in the expanded version.
Number 2, Section C: Something cannot bring itself into existence. In order for something to bring itself into existence, it has to have attributes in order to perform an action. But if it has attributes, then it already has existence. If something does not exist, it has no attributes and can perform no actions. Therefore, something cannot bring itself into existence.
Here's where we get to the point.
Many theological arguments are structured as follows:
1) This rule exists, applies to everything, and cannot be broken.
2) Something must have broken this rule, because it's difficult to conceive another way the universe could come to be.
3) It must have been God.
That's called special pleading. God is exempt from whatever rule it is that they put forward, because he's God. Why is it God that's exempt, and not, say, the universe? Which god is the one that's exempt - Ymir? Nox? Yahweh? Brahman? How do we know such an entity thinks marriage is between a man and a woman? Why did it create cancer?
These can all essentially be broken down to, "Who designed the designer?" Once you ask that question, the special pleading is revealed for what it is, and their efforts to arbitrarily assign a sort of "stopping point" to the logical regression comes to a screeching halt.
There's a decent chance my next post will deal more with the Transcendental Argument. I apologize for that. It's complicated, confusing, and very weird. That, in my opinion, is precisely why some people find it so convincing. It's a logical magic trick.