That is a very good question.
First, this question and its resulting answer from the Reformed perspective has been argued on this board ad infinitum, ad nauseum. So, I am not explaining anything new that you have not heard before. That said...
We know that the sinner is, as scripture explains, "dead in your trespasses and sins" (Eph. 2:1). The word Paul uses for dead is νεκρός (nekros). It means dead as in a corpse, not being in a state of death. There was purpose to that word selection by Paul. Someone who is dead is incapable of doing anything.
Paul alludes to this in his first letter to the Corinthians:
But a natural man does not accept the things of the Spirit of God, for they are foolishness to him; and he cannot understand them, because they are spiritually appraised.
New American Standard Bible: 1995 update (1 Co 2:14). (1995). The Lockman Foundation.
The natural man is the worldly man - the unregenerate and unsaved man. Because the natural man does not have the Spirit of God, he is incapable of understand spiritual truth.
So, if the natural man - the sinner - is dead and does not understand, something outside of man has to make him capable of belief/faith. Paul deals with this directly.
But God, being rich in mercy, because of His great love with which He loved us, 5 even when we were dead in our transgressions, made us alive together with Christ (by grace you have been saved),
New American Standard Bible: 1995 update (Eph 2:4–5). (1995). The Lockman Foundation.
We see that it is God who unilaterally chooses to make the one who is dead alive. We get into the
ordo salutis (order of salvation) at this point. Regeneration (some call it "enlightenment") precedes faith but it does not eliminate faith. Once regenerated the individual exercises saving faith (belief).
Now, we can get into the means of salvation. You quoted Romans 10:17 which I affirm. The Gospel is the means of salvation. However, the means is not the same as the internal work of the Spirit. The Spirit uses the means (the Gospel) as part of the outward call.
OK. I did not want to get too deep in the weeds. Mission
not accomplished. But you asked.
Have a blessed evening.