1. If Jews could be saved by the Old Covenant, there would have been no need for Jesus to preach to the Jews. He would have gone straight to the Gentiles.
2. If the Old Covenant, or merely being a "good person", could save people, His sacrifice on the cross would have been a cruel farce.
Consider Matthew 26:39
After walking a little farther, he quickly bowed with his face to the ground and prayed, “Father, if it’s possible, let this cup ⌞of suffering be taken away from me. But let your will be done rather than mine.”
God would have been saying to Jesus, "Sure, there are plenty of ways for people to be saved. Follow the Old Covenant. Or just be a good guy. But it's nice to give people a choice. So go ahead and suffer anyway."
I'm not Catholic so I don't put much weight to him or his denomination (especially after the Pachamama incident). But I believe God will all judge us all by our deeds according to the light we are given.