There is a common misconception in the world, and even among Christians, that the Old Testament is about works and the New Testament is about Grace. The idea is that somehow, people in Old Testament times were actually saved by physical acts of obedience rather than by a heart change brought about by God Himself.
This is a tragic misunderstanding.
The reality is that the means by which God brings people into His own presence has always been the same, Jesus Christ on the Cross. Romans 3 makes that clear. God could overlook “former” sins (sins of the past) because Jesus paid for all the sins of all God’s people for all of time. God has always been about changing hearts not simply changing behaviors.
The beginning of Deuteronomy 30 illustrates this clearly. It says:
 And the LORD your God will circumcise your heart and the heart of your offspring, so that you will love the LORD your God with all your heart and with all your soul, that you may live.  And the LORD your God will put all these curses on your foes and enemies who persecuted you.  And you shall again obey the voice of the LORD and keep all his commandments that I command you today.
(Deuteronomy 30:6-8 ESV)
There it is. The Lord will circumcise the hearts of the people so that they will obey. That is always the order of things. He changes us from the inside and our outward lives reflect that change. Over and over again, the Old Testament says that the Lord does not desire sacrifices, He desires obedience from the heart, and He is the one who brings that about.
We must ask Him to change our hearts, for when we ask Him for what He desires, He answers with a resounding yes. He wants to change hearts. He desires all to come to know Him. He loved the world so much that He gave Jesus Christ as a sacrifice so that we might live if only we place our trust in Him, and He is infinitely trustworthy.