No, in verse 1 he mentions Israel, they are not the subject. The letter is all whom be in Rome (see 1:7). The subject is faith in general. The faith the just live by, which establishes the Law.
This faith according to the context Israel as a whole did not have. (see 9:30-33). The Gentiles were living the righteousness which is of faith that establishes the Law (see 9:30). This is the context
Chapter 10 describes what this faith is that Israel was not experiencing.. It says The word is nigh unto you in verse 8. The You are the all that be in Rome to which the letter is was being written. That would be Jew and Gentile.
Verse 8 continues to speak on this faith the gentiles where living by the establishes the law and says that it is in their hearts and in their mouths. And closes that statement with, that is the word of faith in which they preach.
Which means the word being in our hearts is the faith through Christ. The changed heart is the faith which the just live by and establishes the law, Because it it believes unto righteousness. as verse 10 states.
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Rom 9:30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
Rom 9:31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
Rom 9:32 Wherefore? Because [they sought it] not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
Rom 9:33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.
Rom 10:1 Brethren, my heart's desire and prayer to God for Israel is, that they might be saved.
Rom 10:2 For I bear them record that they have a zeal of God, but not according to knowledge.
Rom 10:3 For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.
Rom 10:4 For Christ [is] the end of the law for righteousness to every one that believeth.
Rom 10:5 For Moses describeth the righteousness which is of the law, That the man which doeth those things shall live by them.
Rom 10:6 But the righteousness which is of faith speaketh on this wise, Say not in thine heart, Who shall ascend into heaven? (that is, to bring Christ down [from above]
Rom 10:7 Or, Who shall descend into the deep? (that is, to bring up Christ again from the dead.)
Rom 10:8 But what saith it? The word is nigh thee, [even] in thy mouth, and in thy heart: that is, the word of faith, which we preach.
Rom 10:9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
Rom 10:10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.