The first covenant, with Abraham, had a sign and seal in the “sacrament” of circumcision. This was applied to males only, but to those who came into the covenant as adults, they had to submit, as well as those born into families which were part of the covenant on the 8th day. This mark, this symbol of having the foreskin removed was not withheld until the child could “choose” or “understand” what was going on. Instead, it was a teaching tool as the sons matured, I can imagine. “Dad, why do we look different than the gentiles?” (Or I at least suppose this is how it went. Now as to how everyone was so aware of everyone else’s foreskin status remains a bit of a mystery to me.)
Nevertheless, the sign of the covenant was given to infants. They were marked. “This one belongs to God.” Why not apply the sign of the new covenant to our children?