If they could initiate infants into the Old Testament Covenant Church of Israel via circumcision, they could certainly initiate Christians into the New Covenant Church---the New Israel by baptism.
(Not really a new Israel but the same Israel as God intended for it to - God's people, the sheep of his pasture, chosen from every language, tribe and nation. After all, the true Israel is and always has been nothing but Jesus Christ himself.)
'Dedication' makes no sense.
No, it makes sense. As bbbbbbb reminds us, there are clear descriptions and instructions on dedicating people, animals, and objects to God in the OT. It's a nice gesture, but dedication is not sacramental in the same way as baptism. It does not convey the same benefits as guaranteed by the explicit promises of God that baptism does.
It does not result in the person being dedicated receiving the fullness of Jesus Christ and everything that comes with him by grace through faith like baptism does. It does not mark the one being dedicated in their body as a child of God, a son of God, as one who has been granted a new righteous nature in Christ apart from their Adamic fleshly sinfulness. It does not mark them as a co-heir with Christ, an undeserving recipient of the gift of eternal life in Jesus Christ Our Lord.
Dedication, ironically enough, actually benefits the one being dedicated only as much as what those who deny God's gift of baptism say that baptism accomplishes - a public confession, an act of obedience (though dedication is not commanded of us in scripture), basically, just a nice thing to do.
Dedication really is more about the parents and those around them who undertake to raise the child as a Christian (even though they would deny that the child can actually BE a Christian until they reach that magical, all-important, yet simply unbiblical age of decision.)
If baptism is as Scripture says "now saves you" and is for 'the remission of sin' as St Peter says in Acts, why not enjoin a baby unto the Body of Christ? There isn't any reason that I can see.
It does, and there isn't.
Actually, if they could initiate female infants into the Old Testament Covenant Church of Israel (a specious appellation if ever there was one) without circumcision,
Specious accusations of specious appellationing aside, the lack of a female sacramental command corresponding to circumcision for males is actually a very interesting point.
While on the one hand we have circumcision, a physical act united with a spiritual truth by clear and certain promise from God, on the other hand we have the fact that God is free to act when and how he so chooses, as when he proclaimed Abraham righteous when he was granted faith to believe God's promise. Thus we have Jewish infant boys being united with God's people through the sacramental act of circumcision, while the Jewish infant girls are united with God's people in the same manner as their father Abraham was even before he was circumcised, as St Paul points out: By God acting to grant faith in his promises, including the promised Messiah, by means of the heard Word of God.
This corresponds exactly to the promises of the new covenant (neatly illustrating the point, btw, that though specific details may vary from the old covenant to the new covenant, Israel and the Church are and always have been one entity). In the Church we have been given the Sacrament of Holy Baptism in which the Word of God, combined with a physical sign, conveys all the spiritual benefits promised by God to those who are baptized. These are sure and certain promises upon which we can rest our hearts and minds and be completely assured that Our God has promised to save us in Holy Baptism, and that God never breaks his promises.
At the same time, however, God does not limit himself from acting in only one way to save sinners through faith in Christ. He has also promised that the Holy Spirit will act when and where he chooses to save sinners through faith in Christ by the hearing of the Word.
they could certainly initiate female Christians into the New Covenant Church - the New Israel (a theological construct) without circumcision or baptism or any other rite.
Yes, as above, it is possible and even commonplace for God to do so. This does not negate the fact, however, that God has given his people a wonderful gift in Holy Baptism by which we may have God's sure and certain assurance of the salvation of our little ones, both for their benefit and for those who love them.
This is where the difference lies. Baptism is a clear and certain promise of God. Outside of the sacrament the hope of salvation exists, but because of the lack of a physical, tangible sign, certainty is more elusive, and the door to fear and doubt is left open to swing in the wind of circumstance.