I'm guessing that you mean, is the possibility of a saving faith inherent in lost persons?
Your question is loaded on many levels.
One: Because it only allows two possibilities, the same two possibilities that Calvinism allows. It's the two options model, which is not Biblical. It's the flesh vs. Spirit, without allowing distinctions in the Spirit. It's born again or the flesh. I can show how that idea is not Biblical by asking you a simple question. One that was posed already but not answered. How did these believe?
John 7:38-39 He who believes in Me, as the Scripture has said, out of his heart will flow rivers of living water." But this He spoke concerning the Spirit, whom those believing in Him would receive; for the Holy Spirit was not yet given, because Jesus was not yet glorified.
And two: Technically a saving faith is the faith that begins with the indwelling of the Holy Spirit. That's what Jesus Authored and Finished. That's the work that He began in us and promised to finish. This is a result of the initial faith and the indwelling. Most people use the term 'faith', especially 'saving faith' very loosely, but in the context of your question I would not. You must distinguish a saving faith from our initial faith, called believing. If you believe, then you will have eternal life (John 3:16). If you believe, you will be saved (Romans 10:9). Technically, a saving faith is always the result of the initial faith. If you think that distinction is unbiblical, then think of the Paul vs. James debate. Paul is speaking of justification, the initial faith, and James is speaking of the evidences of faith (life), the fruit of the Spirit, the ongoing faith. OT believers had the initial faith, but did not have the ongoing, because they did not have the Spirit in them. None good, no not one (no Spirit).
You are playing both sides of the fence in the way you use "saving faith", counting it all as one, not because the Bible says to, but because Calvinism says to. By saying "saving faith', one can mean initial faith (cause) or one can also mean ongoing faith (life) , but they are two different questions, and you're trying to blend them into one.
Is prevenient grace inherent or a gift from God? Both, prevenient grace allows both man to chose, and God to give.