The scriptures teach us that no one could keep the law but that the law was given to show Israel their sinfulness and their need for a Savior (Messiah/Jesus). Yet you say they were required to keep the law – is this not a contradiction?
I am not the one who says that. In Hebrews 10:8 it says that God did not desire their sacrifices and offerings but the Law required them to be made. What God desired was an end to sin, but until the Redeemer came to solve the sin problem permanently, the sacrifices and offerings required by the Law set their sins aside temporarily so He would not have to judge them. So the Law both revealed their sins and provided a temporary remedy for them. Keeping it was evidence of their faith in a coming Redeemer who would save them permanently.