You can be confident about a child’s profession of faith in a Reformed church because of the Reformed Tradition’s emphasis on children in worship. I don’t care what kind of revisionist history you come up with, if you grew up in the late 20th century or the first decade of the 21st, unless you were in a Reformed church, you did not think much about this issue.
I am thankful for the Family-Integrated Church movement. Though I disagree with them on several things, they did help me in particular to think about this issue when I had not been doing so before. And what I found out was that the Reformed tradition has always believed children of all ages should be involved in corporate worship.
The biblical evidence is overwhelming for children (even infants!) being involved in corporate worship: Exodus 12.1-28, Deuteronomy 4.9-11, Deuteronomy 6.1-9, Deuteronomy 31.9-13, Psalm 78, Ezra 10.1, Nehemiah 12.43, Joel 2.12-17, Acts 2.42, Acts 16.33, Ephesians 6.1-3.
What you most definitely will not find in the Bible is any teaching on “Make sure you get the children away from the room when the sermon starts!”
I’m not saying there is not some wiggle room for freedom. I’m not saying this is easy. I’m not saying I have it all figured out.
I am saying that Christians should teach their children to worship God and listen to the preaching of the Word. It takes training and hard work and discipline and prayer. But if a 7 year old has sat under the preaching of the Word for almost 5 years, has seen the preacher’s pleas, has heard the songs and prayers of the saints, has become acquainted with the creeds and confessions and catechisms of the Church, has seen the Lord’s Supper observed each week, and week by week, month by month, year by year, has grasped a little bit more of who God is, what sin is, who Jesus is, and how we can be saved– is it really that surprising they may express faith, and that faith be real?