“And He gave him the covenant of circumcision: and so Abraham begat Isaac and circumcised him the eighth day; and Isaac begat Jacob; and Jacob begat the twelve patriarchs” (Acts 7:8)

Here we see that God made a covenant with Abraham and called it “the covenant of circumcision.” A covenant represents an arrangement whereby two parties coming together agree to certain promises, stipulations, and privileges or responsibilities. In Abraham’s case it was ALL OF God determining to give Abraham a seed from whom all the nations of the earth would be blessed.

Circumcision was the sign of the covenant for two reasons.
First, as circumcision is practiced on the male child, it was a sign that the Promised Seed, would be a man-child, the God-Man. It is of note that the Scripture records the circumcision of the LORD Jesus as a baby on the eighth day, according to the law, at which time He was officially named, Jesus, according to the instruction given by the angel to Joseph and Mary, Luke 2:21. Galatians 4:4-5 - “But when the fullness of the time was come, God sent forth His Son, made of a woman, made under the law, to redeem them that were under the law, that we might receive the adoption of sons.”

Second, the cutting away of the flesh was representative of the work of the Man-child in the putting away of the body of sinful flesh, by His sacrificial death on the cross (Colossians 2:11). Some commentators have noted that this was the first time the blood of Christ was shed. While not the shedding of blood unto death, required for the satisfaction of God’s law for the sin of His people, yet it did show Him to be truly man, although fully God. This foreshadowed the complete shedding of blood unto death at the cross, that the apostle Paul also was directed of the Spirit to describe as a circumcision, not made with hands, Colossians 2:11. Even as in physical circumcision there is a removing of flesh, so in Christ’s death, a removing of the body of the flesh (putting away of sin) there at the cross, by which God the Father once for all justified forever every one for whom Christ died.

The writer to the Hebrews makes the full connection between God’s initial instruction to Abraham to circumcise every male child one the eighth day, Genesis 17:10, and the coming of Christ, taking on the ‘seed of Abraham,’ to redeem and reconcile them as sinners to God the Father. Hebrews 2:16-17.

There is no question that the LORD Jesus fulfilled all that was written of Him in the law. So complete was His work of salvation, that there remains no longer any requirement of the law, such as circumcision, or any other ceremony. In fact, as Paul so forcefully declared to those of his prior religious faith who sought to make circumcision yet to be an obligation, “Behold, I Paul say unto you, that if ye be circumcised, Christ shall profit you nothing,” (Galatians 5:2).

This also applies to any who would replace circumcision with a rite of baptism or any other ordinance. The Spirit directed the apostle to write just as clearly, "I do not frustrate the grace of God: for if righteousness come by the law, then Christ is dead in vain," (Galatians 2:21).

Any work of the flesh, for the cutting away of the flesh of sin spiritually, by whatever method or thought it may be, no matter how right it may seem to those who practice such methods, is a denial of the death of the LORD Jesus, and His FINISHED WORK of the circumcision of the body of sin for His people at the cross.

The conclusion of the Gospel of Christ is clear. “For in Christ Jesus neither circumcision availeth anything, nor uncircumcision, but a new creature. And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God,” (Galatians 4:15,16). There is a clear connection between the ‘new creature,’ and ‘the Israel of God.’ The new creature (the Israel of God) is the church of the LORD Jesus made of up Jew and Gentile, made ONE in Christ.
"Having abolished in His flesh the enmity, even the law of commandments contained in ordinances; to make in Himself of two one new man, so making peace,” (Ephesians 2:15).