Those who truly have been saved will persevere. Eternal security. That's what these passages are saying. But they're not saying that God first saves, and then comes faith.
Romans 10:9 If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. 10 For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved.
When asked, the apostles gave the logical order of belief and salvation.
Acts 16:31 They replied, “Believe in the Lord Jesus, and you will be saved—you and your household.”
If it were as you say, salvation then faith, he would not have answered this way.