Aged 6 to 14 you write, under the law of the land children in that age range are not mature enough to enter into a legally binding agreement yet you treat their baptism as valid according to credo-Baptist standards
Faith isn't a legally binding agreement. It is a gift of God and the work of the Holy Spirit. So yes, children as young as 5 or 6 can have faith. It is a childlike faith that may not be fully formed, but it is faith nonetheless. Baptism is a marker in the faith journey that takes place at the beginning of the journey.
If, as your post reasons, a child of 6 can make a credible profession why do you preclude an infant from making one? Is it because you cannot hear them speak in a language that you can understand?
It is because they do not have the intellectual capacity to even have a childlike understanding of the Gospel and therefore cannot have a personal faith.
Here is how most baptisms of children play out.
A child is raised in church and exposed to the gospel/Bible repeatedly.
At some point, the child will start asking questions about Jesus, sin, and salvation. Many times at this point the parent will bring in a Pastor or counselor to answer the child's questions. This process can happen over weeks, months, even years. Sometimes the questions are answered and the child goes "Okay" and never says anything else about it. If that happens the parent/pastor keep praying for the child to come to faith.
Sometimes the child will tell his parents/pastor that they believe/want to be forgiven/want to trust Jesus. At this point the parents will take the child to a pastor (if it has not already happened) and the Pastor will talk with the child and attempt to ascertain the credibility of the child's profession. If both the Pastor and Parents are in agreement that the child's faith in genuine then they will discuss baptism. Oftentimes, they will decide to wait on baptism in order to further discern if the child has come to faith or is just wanting to please his/her parents or because he thinks it would be fun to be baptized. If it is obvious that the child really believes (to the best of his/her ability) then baptism will be scheduled. If at any point the child says "I don't want to be baptized" then they are not.
Oftentimes, when children get older and start questioning their faith the ability to remember being baptized can be a powerful reminder to how they personally experienced God's transformative grace.