Christ the perfect man was not destined to die in the same way as Adam before the Fall was not destined to die. After the Fall without access to the Tree of Life sickness and mortality became to lot of mankind. Whilst mankind had no power over death Our Lord did and overcame it by raising Himself from the ‘dead’.
Yes, the Eucharistic Sacrifice, the same Sacrifice that He offered upon the Cross the following day was  established in an unbloody manner before His  death, the selfsame unbloody Sacrifice that is is offered every time He offers it through one of His priests at Mass.