Thats what we Calvinists are trying to say, though sometimes, I suspect, our words get in the way.
It isn't complicated when you follow what the Bible says, 'faith cometh by hearing and hearing by the word of God'.
Only the Calvinistic notion of total inability (not depravity) makes Regeneration necessary before faith, since a spiritual 'dead' man cannot believe anything about God until he is first born again.
That is not a 'logical' point, that is a 'theological' point, which separates Calvinists from non-Calvinists who believe in salvation by faith and faith alone and then one is regenerated, justified, redeemed, adopted, etc.