No, it is not possible for mankind to restore the Sun to its full youthfulness after it has died from old age. The Sun is a finite source of energy, and eventually it will run out of fuel. This will result in the Sun cooling and expanding, ultimately becoming a white dwarf. Restoration to its youthful state would require the input of an amount of energy greater than the total energy the Sun has ever produced, which is not possible with current technology and understanding of physics.