The cosmological argument is often misunderstood. The argument isn't "everything that exists needs a cause, therefore God is the cause", but rather, everything that began to exist needs a cause, and thus, there must be an uncaused cause.
This is sometimes illustrated by a long line of dominoes. Our existence is represented by a red domino falling over. If everything needs a cause, the red domino would never fall over because the dominoes needed to knock it over will never finish being set up. Thus, the fact that the red domino has fallen proves that there has to be a first domino.
If we ask "if God created everything, what created God?", God ceases to be the first domino and instead ends up being the second, or third, or fourth and so on and so forth. Effectively, all this question does is changes God's status from the first cause to an effect.
But Biblically speaking, nothing created God, not in the sense that God just randomly jumped into existence, but in the sense that there was never a time when God did not exist. In multiple places in the Bible, God's eternal nature is described. God is said to be the "first and the last", "from everlasting to everlasting", and "the same yesterday, today, and forever". Even God's most famous name, "I AM", suggests eternality. Basically, the God of the Bible has no more of a beginning than an end. When does forever end? Never. When did God begin? Never. God just is.
This makes God the perfect candidate for the Creator of the universe. Other things, such as the Big Bang, are finite. It's perfectly reasonable to ask "if the Big Bang created the universe, what caused the Big Bang?", because the Big Bang is as much an effect as a cause. Explosions don't just happen (neither do explosions typically create order, but we won't get into that). But God does not need to have His origins explained, because God is the uncaused cause.