Hello Eleanor, you mentioned Acts 16:34 but you had other passages that you could have referenced. On 5 occasions in the NT “household” is mentioned in relation to “baptism.” By Paul once and by Luke 4 times.
First Paul’s:
1 Cor 1: 16 (Yes, I also baptized the household of Stephanas; beyond that, I don’t remember if I baptized anyone else.)
Later in that epistle Paul mentions the household of Stephanas again:
1 Cor 16: 15 You know that the household of Stephanas were the first converts in Achaia, and they have devoted themselves to the service of the Lord’s people. I urge you, brothers and sisters, 16 to submit to such people and to everyone who joins in the work and labors at it.
As such (in the 16 Chapter) for Paul “household” = a body of persons who can a) convert, and b) devote themselves to service. Newborns can’t do either and as such, Paul’s use of “household” in 1 Cor 16:15 would not include newborns…and if Paul was consistent, then his use of “household” in 1 Cor 1:16 would also not include newborns.
Now Luke’s:
Crispus’ Household (Acts 18:8):
Then Paul left the synagogue and went next door to the house of Titius Justus, a worshiper of God. 8 Crispus, the synagogue leader, and his entire household believed in the Lord; and many of the Corinthians who heard Paul believed and were baptized.
Since newborns can’t believe, either Crispus’s “household” did not include any newborn(s) or Luke was expecting that his readers would employ common sense and understand that for him, in that context, “household” only included those capable of belief.
Philippian Jailer’s Household (Acts 16:31-34) :
They replied, “Believe in the Lord Jesus, and you will be saved—you and your household.” Then they spoke the word of the Lord to him and to all the others in his house. At that hour of the night the jailer took them and washed their wounds; then immediately he and all his household were baptized. The jailer brought them into his house and set a meal before them; he was filled with joy because he had come to believe in God—he and his whole household.
For Luke here “household” = a body of persons who could believe. Newborns are incapable of forming belief and as such, Luke’s use of “household” in Acts 16: 31-34 would not include newborns.
Lydia’s Household (Acts 16:15)
Acts 16: 14-15 One of those listening was a woman from the city of Thyatira named Lydia, a dealer in purple cloth. She was a worshiper of God. The Lord opened her heart to respond to Paul’s message. When she and the members of her household were baptized, she invited us to her home. “If you consider me a believer in the Lord,” she said, “come and stay at my house.” And she persuaded us.
As pointed out above, Luke’s use of “household” later in this chapter meant a body of persons who were capable of belief. As such, why would we assume that earlier in chapter 16, Luke used household in a different fashion?
Cornelius’ household (Acts 10/11)
Acts 11:He told us how he had seen an angel appear in his house and say, ‘Send to Joppa for Simon who is called Peter. He will bring you a message through which you and all your household will be saved.’ 15 “As I began to speak, the Holy Spirit came on them as he had come on us at the beginning. 16 Then I remembered what the Lord had said: ‘John baptized with water, but you will be baptized with the Holy Spirit.’ 17 So if God gave them the same gift he gave us who believed in the Lord Jesus Christ, who was I to think that I could stand in God’s way?”
Acts 10: 44-47 While Peter was still speaking these words, the Holy Spirit came on all who heard the message.The circumcised believers who had come with Peter were astonished that the gift of the Holy Spirit had been poured out even on Gentiles. For they heard them speaking in tongues and praising God.
Then Peter said, “Surely no one can stand in the way of their being baptized with water. They have received the Holy Spirit just as we have.”
I have reversed the order of the passages b/c chapter 11 is a report on how Peter was called to Cornelius’ house and chapter 10 records what happened after he got there and preached. The passage doesn’t say that a household was baptized, but rather that all the household would be saved. The progression is: heard the message => received the Holy Spirit => were baptized. Hearing the message is not something that newborns are capable of doing.
In conclusion then, the “household” passages DO repeatedly connect baptism with a concurrent belief and DO NOT indicate that infant baptism was conducted during the NT era.