I disagree. It is a fundamental origins question.
For the record, I lean toward invention for axioms and discovery for the implications of the axioms.
Your belief has some problems. Historically, secular mathematicians have agreed that we should have absolutely no expectation that our invented axioms would have any application in the real world. The fact that over and over again they do is what Einstein referred to as a "miracle".
Axioms are selected because they are effective in the real world. But when the boundaries of the real world expand due to experience, the axioms begin to fray at the edges.
We cannot imagine violations of the fundamental axioms of arithmetic because we have no experience with exceptions. Arithmetic is an extension of counting, and we do not experience anomolies in the process of counting.
We have experienced anomolies in geometry, leading to adjustments in the axioms of geometry. Imagine trying to explain to the ancient Greeks that the geometry of relativity describes the real world.