Exactly, If one confesses with the mouth that Jesus is the son of God born in the flesh and that he died for the sins of mankind and was raised to life again and if they believe in their heart that they are saved by his grace then they are truly born again.
Notice the word if not when, in fact in all the verses of salvation the word if is most used not when. If it all was predestined to begin with then why use the word if not when?
The scripture that you are attempting to quote is Romans 10:9-10. By keeping the chapter in context, we have to go back to verse 1 to determine who Paul is talking about, which is Jacob/Israel. God changed Jacob's name to be no more called Jacob, but to be called Israel. Gen 33:28. Jacob/Israel is representative of God's elect, Rom 9:11.
In verse 1 Paul is praying that God's eternally saved (delivered) elect will be saved (delivered) from their lack of knowledge of the gospel. Saved, according to Greek interpretation, means "delivered". Besides our eternal deliverance, there is deliverances that we receive as we sojourn here in this world. The lack of separating the different "deliverance"(salvations) will cause one to interpret the scriptures to teach "eternal salvation by the good works of man".
We receive deliverance here in this world by our good works, but we, only, receive our eternal deliverance by God's sovereign grace, without the help of man's good works.
Because of the "zeal of God" in verse 2, indicates that these people were already born again believers in God, and in verse 3, by not receiving the knowledge of the gospel, they were going about to establish their own righteousness, by their good works, having not submitted themselves unto the righteousness of God.
In verse 10, Paul is addressing the same born again children of God, to believe unto the righteousness of God, and confess with their mouth to be delivered (saved) from their lack of knowledge of the righteousness of God, with the understanding that they have the imputed righteousness of Christ.
I realise that this is a lot to absorb at one time, but to me, this harmonizes with all of the other scriptures. The preserved and inspired scriptures are intended by God to be instructions to his elect (born again believers) on how God wants his children to live their lives, as they sojourn here in this world.