I would say they were always under grace, God has always dealt with mankind by Grace. We know this because of the great murderer and adulterer who was also called the friend of God. As David said, Sacrifice and burnt offering you did not desire.
What the law did was show man he needed God. He was able to see his sin, and had no excuse. He was also shown the way to redemption. The murder or slaughter of the lamb.
Grace is a characteristic of God. God does not change like shifting shadows; so I agree with you that he was as much a graceful God in the OT as he is now. However, the Law was devoid of grace. Every sin had to be paid or atoned for.
David received God's grace and forgiveness because he repented. However, he could not stop the consequences of his sins. He lost his child through Bathsheba. His son, Absalom plotted against him and slept with his wives...etc
We, who are under the New Covenant, have been freely and generously given the grace of God (Eph 1:6-8) through Jesus, who was the atoning lamb sacrificed once and for all.
The law left man (including us) without excuse. It showed man that he could not make it on his own without the grace of God. Therefore no one can say, "I can attain salvation by my own works." If anyone says this, he must be told about the huge failure of Israel, who tried to do the same thing.