REASONING ABOUT THE COSMOS
A posteriori arguments are rooted in the real world of experience and prove that things exist in that real world. If the Cosmological Argument is an a posteriori argument then it is adding to our synthetic knowledge of a world which has God in it, not just describing that world in a different way.
A posteriori arguments gain support from evidence. Scientific investigation reveals contingent features about the universe: it has a beginning (the "Big Bang"), it's expanding and changing, there are laws of cause-and-effect. The more we learn about these things, the more persuasive the Cosmological Argument becomes.
God is not a "thing" that exists "in" the physical world. For many believers, God is a transcendent being that exists outside of time and space. This makes proving God's existence a bit more like a mathematical proof (like Pythagorus or pi) instead of weighing up physical evidence.
The world is too varied to produce evidence for or against God. The Cosmological Argument "cherry picks" signs of cause and contingency, but what if there was another universe before the "Big Bang"? Why stop there? Why shouldn't there be an endless string of universes expanding then dying and new universes starting over. This would be an infinite regress.