I am legally deaf so I know "hearing" is not the same as "hear". 1 Thessalonians 1:5 "because our gospel came to you not simply with words (hearing the gospel), but also with power, with the Holy Spirit and with deep conviction. You know how we lived among you for your sake." The Holy Spirit convicts a sinner to be saved when they "hear" the gospel. That's how I understand Romans 10:17 when Paul wrote, Consequently, faith comes from hearing the message, and the message is heard through the word of Christ. Looking at Romans 10:17 says in the original Greek, "Faith comes by hearing a speech about Christ." Faith comes by hearing a speech about Christ, not a subjective analysis about what's going on in yourself.
The difference between "accepting" and "conviction" is the actual conversion. I want to go back to Paul's question in Galatians 3:2 "This only I want to learn from you: Did you receive the Spirit by the works of the law (accepting-decision), or by the hearing of faith (conviction) ?" Understanding and accepting faith is one thing and 'actual conversion by the conviction of the Holy Spirit' is another. Not our understanding nor our decisions but rather the Holy Spirit is within us believers, Christ dwells in our hearts, and "Christ in you, the hope of glory" (Colossians 1:27) is the burning core of the Christian faith.