Baptism brings us into the New Covenant.
In Judaism offspring were born into the covenant.
While I believe Baptism is an element in which we enter into the New Covenant, talking about Judaism can become just as complex as baptism.
For instance, the essence of Judaism comes through the mother while the identity comes from the father. If a non-Jewish mother marries a Jewish man, the child needs to go through conversion. However, if a Jewish mother marries a non-Jewish father, then the child is considered a Jew.
As for covenant, Circumcision was a sign of that covenant.
Baptism brings us into the New Covenant.
In Judaism offspring were born into the covenant.
In Christianity offspring are born from above (John 3:5) into the New Covenant, a member of the Church, a member of God's kingdom as brian100 said in the OP.
And Peter said to them, “Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit. For the promise is to you and to your children and to all that are far off, every one whom the Lord our God calls to him.” (Acts 2:38-39 RSV)
I think context is in order when talking about those in Acts 2. If we go back, we read.
Acts 2:13 But
others mocking said, They are filled with new wine.
Others in verse 13 were those who opposed and mocked. But who are these "
others".
It is of note that they did indeed see the truth ("They are filled with new wine."), but they didn't understand it, so they mocked it.
Acts 2:14 But Peter, standing up with the eleven, lifted up his voice, and spake forth unto them, saying,
Ye men of Judaea, and all ye that dwell at Jerusalem, be this known unto you, and give ear unto my words.
Peter is speaking to a specific subset of Jews considered in verse 13 as "others". These "
others" were of Judaea and Jerusalem.
And who might these "
others" be. If we go back to the Crucifixion in Matthews accout, I believe we can shed some light on who these "
others" were to whom Peter is addressing in Acts 2.
Matthew 27:24-25 So when Pilate saw that he prevailed nothing, but rather that a tumult was arising, he took water, and washed his hands before the multitude, saying, I am innocent of the blood of this righteous man; see ye to it.
And all the people answered and said, His blood be on us, and on our children.
This gives us an idea why Peter says,
Acts 2:39 For to you is the promise,
and to your children
If we look at Acts 2:38, I think it's good to note:
And Peter said unto them,
Repent ye, and be baptized every one of you in the name of Jesus Christ unto the
remission of your sins; and
ye shall receive the gift of the Holy Spirit.
Acts 2:39 points forward to the promise because Acts 2:38 points to the now. What we do now is important. But furthermore, each one of us needs to make a choice now which will effect the future.
Acts 2 is couched in Torah teachings, which the Jews understood well.
Exodus 34:7 Keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty; visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation.
But this is another teaching.