He could not have, had He only been a good man who came into existence himself nearly 2,000 years ago, died, and remained dead.
But if God, in Christ, enabled punishment for all sin ever committed to be borne by that sinless one, then His resurrection from the dead proved Him to truly be the Son of God, then He could have.
It's all about how God manifests His righteousness to save the unrighteous, yet without violating His own law, that all sin must be punished. It's about justice that is breath-taking in its scope. Because we humans cannot see further than the ends of our own noses (spiritually speaking), we just cannot see it. That is where we need to come to Christ, to learn of Him, for He is humble and His yolk is easy and His load light.
Only once we discover just who it was, dying for our sins on that cross, will we understand. It was God, in Christ, doing what we could never do to be released from our slavery to sin. The Son of God became fully human in order to fully represent all humanity, while remaining fully divine to have the magnitude of deity needed to deal with all sin, forensically, in one action. You have to grasp that this Jesus - the Jesus of the Bible, not the Jesus of the Qur'an or the Book of Mormon or of the Jehovah's Witnesses - was eternally the Son of God from before creation. That He made everything that was made, then became flesh as the virgin Mary's child. Study the first chapter of John's gospel account, then read on to the end. That account was written "that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name." (John 20:31)