A child’s simulated birth may presently be rectified

Dear PAO,

Ten years ago, my wife and I planned to adopt the newly born baby of my distant relative. However, we deemed legal adoption to be expensive and tedious, so we just made it appear in the birth certificate of the baby that he was our child. I then learned that simulating one’s birth is a criminal act. Can the simulated birth certificate still be rectified in order to avoid any criminal liability?