Why did God originally establish a sacrificial system before sending the Messiah?

The temple sacrificial system was basically a shadow type in the OT, pointing to the true type in Christ in the NT.

Hebrews 10:

1 For since the law has but a shadow of the good things to come instead of the true form of these realities

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Why was the sacrificial system of law only a shadow?

it can never, by the same sacrifices that are continually offered every year, make perfect those who draw near.

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It had only a temporary effect. It had to be repeated over and over again. It was not perfect.

2 Otherwise, would they not have ceased to be offered, since the worshipers, having once been cleansed, would no longer have any consciousness of sins? 3 But in these sacrifices there is a reminder of sins every year. 4 For it is impossible for the blood of bulls and goats to take away sins.

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It was not the perfect solution to the problem of sin. For that, God had in mind another solution for the Jews and Gentiles.

5 Consequently, when Christ came into the world, he said,
“Sacrifices and offerings you have not desired, but a body have you prepared for me;

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Animal sacrifices were contrasted with Jesus' sacrifice.

6 in burnt offerings and sin offerings you have taken no pleasure. 7 Then I said, ‘Behold, I have come to do your will, O God, as it is written of me in the scroll of the book.’”

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The perfect solution was sending the Messiah to die for sins. God hinted at that solution in the OT.

8 When he said above, “You have neither desired nor taken pleasure in sacrifices and offerings and burnt offerings and sin offerings” (these are offered according to the law), 9 then he added, “Behold, I have come to do your will.” He does away with the first in order to establish the second.

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The true solution replaced the shadow solution. After the Messiah had died on the cross, Rome destroyed the temple and its sacrificial system.

10 And by that will we have been sanctified through the offering of the body of Jesus Christ once for all.

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Unlike the repetitive old system, the cross was the once-for-all perfect solution.

11 And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins. 12 But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, 13 waiting from that time until his enemies should be made a footstool for his feet. 14 For by a single offering he has perfected for all time those who are being sanctified.

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That's the good news. Not only was the sacrificial system replaced, but the legal system as well.

15 And the Holy Spirit also bears witness to us; for after saying,
16 “This is the covenant that I will make with them after those days, declares the Lord: I will put my laws on their hearts, and write them on their minds,”

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The external legal code no longer bound believers. God sent the Paraclete to dwell in our spirits (hearts and minds).

17 then he adds,
“I will remember their sins and their lawless deeds no more.”

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Can you believe this: God will not keep an account of our sins!

18 Where there is forgiveness of these, there is no longer any offering for sin.

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There is no longer any requirement for animal sacrifices.

Why did God originally establish a sacrificial system before sending the Messiah?

God commanded the Israelites to establish a sacrificial system to demonstrate his holy judgment about sin, sacrifice, and death. In terms of typology, God knew it was only the shadow solution to the problem of sin, but it pointed to the perfect solution, which was Christ's sacrifice.