No, the earth cannot push an object forward with a reaction force. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. In this case, the earth exerts a downward gravitational force on the object, pulling it towards the center of the earth. The reaction force to this is the object exerting an equal and opposite upward gravitational force on the earth, pushing it away. However, since the earth has a much greater mass than the object, its acceleration due to the object's force will be negligible, and it will not move forward.