Actually under Calvinism a person is elect to eternal life prior to the person being born, which is prior to faith. And since the person is born elect to eternal life, he is born saved under Calvinism.
Under Calvinism salvation is not by faith. It's by a pre-birth election. As such it's Calvinists who are attacking salvation by faith alone, seeing as under Calvinism faith is not a precondition for salvation.
In Calvinism, they are not born saved, it is just they are elected to be saved. faith is still a requirement, as is being born of God. The scriptures clearly says, all that the Father gives to Christ will come to Christ. Which means those not given, will not come to Christ and be saved.
God is the chooser, not the will of the man. God does not choose everyone or everyone would come to Christ and be saved.
John 6:37 All that the Father gives Me will come to Me, and the one who comes to Me I will by no means cast out.
Romans 9
14 What shall we say then? Is there unrighteousness with God? Certainly not! 15 For He says to Moses, “I will have mercy on whomever I will have mercy, and I will have compassion on whomever I will have compassion.” 16 So then it is not of him who wills, nor of him who runs, but of God who shows mercy.
God does not personally show mercy to everyone to be granted to come to Christ.
People who do not believe in Christ, God has not granted them to come to Christ. I speak in absolute terms here, meaning they could be granted later, but unless God grants them to come to Christ, they will not believe. Jesus is VERY CLEAR, only by severe scripture twisting can these truths be denied.
61 When Jesus knew in Himself that His disciples complained about this, He said to them, “Does this [o]offend you? 62 What then if you should see the Son of Man ascend where He was before? 63 It is the Spirit who gives life; the flesh profits nothing. The words that I speak to you are spirit, and they are life. 64 But there are some of you who do not believe.” For Jesus knew from the beginning who they were who did not believe, and who would betray Him. 65 And He said, “Therefore I have said to you that no one can come to Me unless it has been granted to him by My Father.”
The SPIRIT gives life, not the flesh, God is Spirit, He determines who is given life, not the man. As Romans 9 so says, not the will of the flesh, the man. We are born of God according to the will of God and also that is why a man is born again prior to faith or being born again would be determined by the will of the man, the flesh.