Your understanding of salvation, faith, and grace relies on a particular and disputable interpretation of Ephesians 2:8-9. Those terms (salvation, faith, and grace) are discussed multiple times in scripture. - you need to do better than that. The only clear case when faith is termed a gift from God is in Romans 12:3 where faith is dispersed to believers for the purpose of service to the rest of the body of Christ.
Romans 12:6 We have different gifts, according to the grace given to each of us. If your gift is prophesying, then prophesy in accordance with your faith;
Romans 10:17 says that faith comes by hearing the word of God and we can all choose what we listen to.
Romans 10;17 So then faith comes by hearing, and hearing by the word of God.
The pattern for salvation in Ephesians 1:13-14 is hear, believe, and sealed,
not sealed, hear, and then believe.
Ephesians 1:13 And you also were included in Christ when you heard the message of truth, the gospel of your salvation. When you believed, you were marked in him with a seal, the promised Holy Spirit, 14 who is a deposit guaranteeing our inheritance until the redemption of those who are God’s possession—to the praise of his glory.
God saves us apart from the works of the Law, and on the basis of His own purpose and grace. If one does not conflate man’s free choice to repent with God’s free choice to save the repentant, then this is not an issue that needs to be reconciled. Humbly admitting you need salvation is not equal to saving yourself. Confessing your sin, even if done freely, does not earn or merit forgiveness for that sin, otherwise, there would have been no need for the cross. God could have just forgiven Abraham of his sin debt because his faith merited it. Even though Abraham believed in God, he still had a debt that he could not pay. God graciously chose to pay that debt through the sacrifice of His Son, without which no one would be saved.
Galatians 3:2 I would like to learn just one thing from you: Did you receive the Spirit by the works of the law, or by believing what you heard?
Calvinists conflate Faith with Works. Per Galatians 3:2, we receive the Spirit by hearing with faith, and hence faith is our introduction to grace. However, from the Calvinistic perspective, any religion that teaches that salvation comes about by anything other than an “Irresistible Grace,” necessarily makes salvation into a works-based process, because (as it is reasoned) once you incorporate any act of the human will—what is left is some element of
human contribution in the process. So, when Calvinists say that “salvation is of the Lord” (Jonah 2:9), what they really mean is that God does everything in salvation, including the act of faith, on behalf of the elect-person, by overcoming their resistance through an irresistible gift of pre-faith regeneration. In other words, Calvinists believe that faith becomes a “work” whenever we come to think of faith as something that we do ourselves, absent of an Irresistible Grace.
This means that in Calvinism, faith without Irresistible Grace = works. There is no discussion of regeneration occurring before faith and there is discussion of Irresistible Grace in the Bible.