How did Timothy become a second-generation Christian who rose to the office of pastor-elder? I believe the answer can be found in 2 Timothy 3:14-15 and I believe that answer provides a template for Christian parents.
"But as for you, continue in what you have learned and have become convinced of, because you know those from whom you learned it, and how from infancy you have known the holy Scriptures, which are able to make you wise for salvation through faith in Christ Jesus." 2 Timothy 3:14-15
There are three parenting lessons in these two verses.
1) Teach Them Early and Often
We know from 2 Timothy 1:5 that Timothy's mother and grandma helped lay the foundation of his faith. These women didn't sit back and wait for someone else to teach this child, they did it. Timothy learned then what Paul was asking him to continue in. Paul no doubt also taught Timothy, but we know from Acts that Timothy had a remarkable faith before he met Paul. Why? Because Lois and Eunice helped him know the holy Scriptures from the time he was a baby. My Bible study partner is going to have a baby at the end of the Summer, my advice to him and to all parents is to start a Bible reading routine right away, before you even think it will make a difference. Timothy heard Bible stories and psalms and wisdom literature and prophesy in his infancy. It is NEVER too early and it's not too late for you to start pouring into your children, your grandchildren, or your friends' kids. This teaching, according to verse 15, makes them wise for salvation. Timothy had a knowledge of the holy Scriptures (Old Testament) that gave him a skill (aka wisdom) to see what the Gospel was more clearly and therefore be saved.
2) They Have to Own It
"... and have become convinced of". Paul says that Timothy learned the truth but then was convinced of the truth. Parents, grandparents, friends and neighbors can't make anyone believe. Prior learning gives our kids a jump start to being convinced. Prior catechism and Bible knowledge helps our children become familiar with the truth, but believing is up to them. Building a foundation isn't brainwashing because Christians are those who are themselves convinced the Gospel is true. Lois and Eunice could have done a miraculously good job of teaching Timothy but the being convinced was in his court. Only God has the authority and skill to perfectly bring all those He desires to a saving faith. Don't try to strap God's burden on your shoulders.
3) You Live Your Greatest Lesson
Timothy's mother and grandma and Paul lived convincing lives. Look at verse 14 again.
"... continue in what you have learned and have become convinced of, BECAUSE you know those from whom you learned it."
Paul gives two reasons why Timothy should continue in what he became convinced of. One is all he knows from the holy Scriptures. The other is because he knows those from whom he learned it. What Paul is saying here is that Lois and Eunice lived a life that showed that Christ's message was true.
"All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, SO THAT the man of God may be thoroughly equipped for every good work." 2 Timothy 3:16-17
Eunice, Lois and Paul lived the "so that" of these verses. What's one way that Timothy was convinced that the Scriptures were God inspired and powerful? He saw what these words and paragraphs and pages and books did in the lives of his mom, grandma and mentor. Their lives were the proof. Just like three healed coronavirus patients begin to convince you that the miracle drug is powerful and effective, so a changed and growing life of righteousness and good deeds proves the ultimate miracle cure.
In conclusion: parents you can do this. Teach them early and often. You don't need to be a theologian, you simply need to do it. Don't burden yourself with trying to do God's work. You lead these kids to water and God will help them drink. And keep a close watch on your life of faith. Your kids life of faith will be taught and caught. Let your life be evidence of God's working. This means that while you're desperately concerned about their faith you must tend yours as well today.