Wrong. You misrepresent Calvinism.
Under Calvinism, salvific faith is the gift of God that is part and parcel with regeneration. That faith is the result of or even the very fact of God in us. It is not we who generate it.
You take the truth of what is said and pervert it to mean what it does not.
Furthermore, your claim that (apparently you suppose is logical) that according to Calvinism there is nothing a person can do, as if you have no responsibility, either you are or are not chosen, so nothing else matters (yes that is the same thing you are saying, if taken to its logical extreme), and that you may as well simply say you are saved from before you were saved --NO, God uses means to accomplish what he set out to do. You may as well say, Christ had no reason to die, since it was all said and done from before Creation. That is by no means Calvin, nor Reformed teaching.
I am not your typical Calvinist, by the way. So I can with impudence note that the Philippian jailer was afraid for his life --not for his salvation, in spite of what the usual Christian use of the verse has been. You will find it hard to prove from the verse and context, that Paul is referring to what Christendom has spiritualized it to say. The principle you hope to prove may well be true. But your text by itself does not support it. But either way, Calvinism does not disinherit belief. It is altogether necessary --in fact, we claim it is unavoidable, that the regenerated will indeed believe. And not only believe but pursue to the end. That does not relinquish anyone of his duty and need to pursue.
You have built a strawman, my friend. Yet it seems even your strawman is near too strong for you to knock down. Do you really think the gift of salvation is free, if there is something you can do, without which it will not be given?