It's a paradox: that which exists is presumed ultimately caused (i.e. brought into existence) by the first cause, which means that the first cause cannot exist because nothing brought it into existence. In other words, the first cause "is" not.
The argument is that you MUST have something UNcaused in order for the universe as we know it to exist.
Your premise creates the problem. The problem occurs IF you state that "nothing can exist that something else brought into existence." Then you are saying "it's turtles all the way down."
You can say that of course, but it's not an argument that effectively refutes the necessity for it. Neither argument is "proven," but one argument at least avoids a nonsensical result, which should be worth something.
:)