So did God show favor to one over another because of what THEY DID by their actions? YES! The Bible says so! Can individuals today carry out actions whereby they can receive the grace of salvation BY THEIR ACTIONS? Yes.
The Bible does state that a sinner must believe. There is no arguing that point. Romans 4:5 "But to the one who does not work, but believes in Him who justifies the ungodly, his faith is credited as righteousness,". The question is whether a sinner believes independent from God or because of God. Paul makes it clear that there are none who seek after God. Romans 3:9-12 "What then? Are we better than they? Not at all; for we have already charged that both Jews and Greeks are all under sin; as it is written, “THERE IS NONE RIGHTEOUS, NOT EVEN ONE; THERE IS NONE WHO UNDERSTANDS, THERE IS NONE WHO SEEKS FOR GOD; ALL HAVE TURNED ASIDE, TOGETHER THEY HAVE BECOME USELESS; THERE IS NONE WHO DOES GOOD, THERE IS NOT EVEN ONE.”" The Apostle also makes it clear that the sinner is spiritually incapable of belief. Ephesians 2:1 "And you were dead in your trespasses and sins,". It is while the sinner is dead in sin, and incapable of faith, that the Holy Spirit regenerates him and makes him able to believe. Colossians 2:13 "When you were dead in your transgressions and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our transgressions". Ephesians 2:4-5 "But God, being rich in mercy, because of His great love with which He loved us, even when we were dead in our transgressions, made us alive together with Christ (by grace you have been saved),"
The action the sinner takes is in response to the work of the Holy Spirit. Salvation does not take place because of any action of man. If even one scintilla of justification was due to something that men do, then salvation is turned into a work. What does the scripture say about that? Romans 4:2 "For if Abraham was justified by works, he has something to boast about, but not before God." So, no, no one "can receive the grace of salvation by their actions".