Nope! Verse 8 says that the word of faith is in the mouths and hearts of men PRIOR to their coming to faith. This excludes some men. Jesus said that the word had "no place" in the Jewish leadership of His day.
You have proven NOTHING. You are wasting your time and energy.
My, oh my! What an example of eisegesis. This is what Rom 10:8 states:
But what does it say? “The word is near you; it is in your mouth and in your heart,” [a quote from Deut 30:14] that is, the message concerning faith that we proclaim (NIV).
To what does 'it' refer? It is the divine righteousness based on faith (Rom 10:6). The utterance/word Paul had in mind when he associated this righteousness with the words from Deut 30:14 was 'concerning the faith' which Paul and others were preaching.
Both examples of 'word' or 'message' (some translations) in Rom 10:8 use
rhema and it means 'the thing uttered' (Lenski 1936:654). It is referring to the word/message that is uttered when it is preached, the content of which Rom. 10:9-11 demonstrates.
We know that the Jews from the earliest days of their lives as children learned the message/word of the Law by memory, so it was put into their mouths and hearts by that means. It was designed to enter the centre of their beings.
The view that you have presented to us in your interpretation of v. 8 is not based on the verse's exegesis. A Calvinistic commentator, William Hendriksen, confirms this in his exegesis of Rom. 10:8,
The apostle continues to "quote" the righteousness that is by faith. The quotation found in Rom. 10:6, 7 ended with the words of Deut. 30:13 [Rom. 10:8]....
There is only one way, however, in which this can be appreciated. That is the way of faith; for God's word, as revealed both in the Old Testament and in the New, is "the word of faith"; that is, it is the word which, in order to exert saving effect, must elicit the response of faith!
Paul now shows that the statement, "the word is close to you; (it is) on your lips and in your heart" is true (Hendriksen 1980:344, bold & underline emphasis added).
There is not a word in this text that says anything about ‘the word of faith is in the mouths and hearts of men PRIOR to their coming to faith’.
Oz
Works consulted
Hendriksen, W 1980.
New Testament commentary: Exposition of Paul's epistle to the Romans. Grand Rapids, Michigan: Baker Academic.
Lenski, R C H 1936.
Commentary on the New Testament The interpretation of St. Paul's epistle to the Romans. Peabody, Mass: Hendrickson Publishers (limited edition by permission of Augsburg Fortress).