If the Son of God had died as a man without shedding his blood, then that would have been a violation of the plan of salvation worked out in the Godhead before any creation started. That is why Hebrews 13:20 speaks of our Lord Jesus Christ being resurrected "through the blood of the everlasting covenant". And in 12:22-24 we learn that those saved will approach heavenly mount Sion, to behold God, the spirits of just men made perfect, "and to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
This indicates that had Jesus not shed his blood sacrificially, he would not have been resurrected. It also says something about the saved in heaven actually seeing that 'blood of sprinkling'.
But, supremely, Revelation 13:8 speaks of those "whose names are not written in the book of life of the Lamb slain from the foundation of the world." In other words, because the Godhead had planned that particular means of salvation, the Son of God could effectively be spoken of as having been slain from the foundation of the world. Because it had been decreed, it was as good as done, for God never has a Plan B. He is in no need of contingency, for what he speaks happens. Creation happened through God speaking matter into existence from that which cannot be seen (Hebrews 11:3) and Christ sustains all creation through the power of his word (Hebrews 1:3). That is why it would have been impossible for Jesus to have been resurrected without shedding his blood, for in the eternal council of God, it was decreed - stated - that the Son of God would become incarnate and shed his blood to save sinners.
The entire book of Hebrews thrashes this out, contrasting the first covenant that was inaugurated with blood, with the new covenant, also inaugurated with blood. The parallels between the old and the new covenants are so powerful, it is unmistakable that the old pointed to the new. The lessons are there, as to why God views life as being "in the blood", and that only a sinless sacrifice of blood can take away our sins, once and for all, with no further sacrifices needed.
"Neither by the blood of goats and calves, but by his own blood he
entered in once into the holy place, having obtained eternal
redemption for us. For if the blood of bulls and of goats, and the
ashes of an heifer sprinkling the unclean, sanctifieth to the
purifying of the flesh: How much more shall the blood of Christ, who
through the eternal Spirit offered himself without spot to God, purge
your conscience from dead works to serve the living God? And for this
cause he is the mediator of the new testament, that by means of death,
for the redemption of the transgressions that were under the first
testament, they which are called might receive the promise of eternal
inheritance. For where a testament is, there must also of necessity be
the death of the testator... Whereupon neither the first testament was
dedicated without blood... [Moses] sprinkled with blood both the
tabernacle, and all the vessels of the ministry, And almost all things
are by the law purged with blood; and without shedding of blood is no
remission. It was therefore necessary that the patterns of things in
the heavens should be purified with these; but the heavenly things
themselves with better sacrifices than these." (Hebrews 9:12-26)
Nobody can read all that the Old Testament says about sacrifices and blood, and not appreciate that that is meant to teach us of the supreme, once-for-all-time sacrifice of the Son of God. That is what the book of Hebrews explains.
Salvation would not have been possible if Jesus had died without shedding his blood, because it was his shed blood that assured his resurrection. No risen Christ - no salvation. The plan of salvation was worked out to the nth degree in the Godhead, before creation started, and - having been decreed by the Word of God - was as good as done. There is never any Plan B in the perfect counsels of God!