Are you saying He fulfilled the Old Covenant with his circumcision?
Yes - but not just with His circumcision. That would be reductive.
Christ fulfilled the Old Covenant and set up the New Covenant with His blood and sacrifice. A piece of that mystery occurs, or is revealed, or prefigured, at the circumcision. Another piece at the presentation at the Temple (40 days after birth). Another piece at His baptism in the Jordan.
But the whole thing - the whole mystery - culminates or is fully revealed at what we call the Passion. This is the term used for those events that took place from The Last Supper up to Christ's death.
I've assembled some passages below. If we were watching a film of Christ's life, we could imagine each of these being read out at both the circumcision and the crucifixion. All except for the last.
God presented Christ as a sacrifice of atonement, through the shedding of his blood — to be received by faith.
also
This is my blood of the covenant, which is poured out for many for the forgiveness of sins.
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Behold! The Lamb of God who takes away the sin of the world!
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Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. For truly, I say to you, until heaven and earth pass away, not an iota, not a dot, will pass from the Law until all is accomplished.
and lastly:
After Jesus had taken the vinegar, He said, 'It is accomplished', and bowing his head he gave up his spirit.
This last passage doesn't fit as a voice-over during the circumcision. Because God's work is not accomplished at the circumcision. But the circumcision is a type or necessary precursor of the Passion.
We must be mindful that the Mosaic law isn't some accidental historical baggage that Christ had to deal with. Instead: it was created for Him and pointed the chosen people towards His salvific death and resurrection.
The Mosaic practice of circumcision was ordained by God because Christ would be circumcised - shedding his blood as a pre-figure of His Passion.
The Mosaic practice of blood sacrifice was ordained by God because Christ the Lamb of God would be sacrificed, at the Passion.
The Mosaic priesthood was ordained by God because one day Christ would be Priest as well as Victim - at the Passion.
And at the Passion the Law is fulfilled, in the sense of being brought to its proper and rightful end.
Christ bows His head. It is accomplished.