First, Rom 10:8 quotes Deut 30:14 -
But the word is very near you; it is in your mouth and in your heart,
so that you may obey it.
In Rom 10:8, the meaning of "the word of faith" is defined by what immediately follows:, namely:
- what Paul was proclaiming about the gospel of grace through Jesus Christ
- that this is claimed by the sinner when conversion occurs and such a sinner acts as follows:
Rom 10:9 - if you confess with your mouth, “Jesus is Lord,” and
believe in your heart that God raised Him from the dead, you will be
saved.
Now, it is obvious that this message of salvation by faith through the grace of Jesus Christ has been proclaimed from the time of Jesus Himself. Therefore, the message necessarily precedes conversion. However, conversion of any sinner, involving such a turning to God, results from the divine miracle of the Holy Spirit on a person as described in many places such as John 16:13 -
But when he, the Spirit of truth, comes, he will guide you into all
the truth. He will not speak on his own; he will speak only what he
hears, and he will tell you what is yet to come.
Now, whether the sinner chooses to accept this gracious offer is another matter. However, earlier in the same book of Romans, Paul says that all are given a revelation of the divine graces (Rom 1:18-22) and many choose to reject it.