You're making many false assumptions. Especially ones that conflict and contradict the clear message of baptism throughout the New Testament.
Your repeated opinions....
1. there were lots of kids in those days (people had many as many died)
2. the parents would want their children saved especially considered that many would not make it to their 5th birthday
are again assumptions completely outside the Word of God.
When we read the passage about Lydia in Acts 16:13-15, there are certain things we know about Lydia and her household.
Things we know about Lydia:
1. She was a seller of purple and she lived in Thyratira.
2. She worshipped God (and therefore is Jewish or a Jewish proselyte?)
3. She heard Paul/Silas speak when she was by the river side.
4. God opened her heart, that she attend to the things Paul said.
5. She was baptized.
6. She besought Paul/Silas saying, “If ye have judged me to be faithful to the Lord, come into my house and abide there”.
7. Paul/Silas stayed at her house, therefore they judged her to be faithful to the Lord.
Things we know about the household:
1. They lived in Thyratira.
2. They were baptized.
The household would not be an atomic family of today’s but larger. It would contain children for the same reasons I’ve stated above.
The fact that they are not mentioned by name and age says nothing but the fact that they were part of the household.
The fact that the UK isn’t mentioned in the Bible is not relevant to the fact that exists.
you says “assumptions outside the Word of God” — first, the WORD OF GOD is JESUS.
Secondly, your assumption that there weren’t kids is an assumption outside the Biblical text. Nowhere does it explicitly say no kids