ZFC has greater consistency strength than PA.
If we take ZFC (or some other set theory) as our meta theory, we can easily see that the axiom of infinity (of ZFC) gives a set of natural numbers (using the von Neumann encoding), which, when equipped with the successor function, is a model of the natural numbers.
zfc doesn't have functions, so you are building something new on top of it.
Also, I am not sure successor function is enough for PA.