Lydia "and her household had been baptized"

On the sabbath we went outside the city gate along the river
where we thought there would be a place of prayer.
We sat and spoke with the women who had gathered there.
One of them, a woman named Lydia, a dealer in purple cloth,
from the city of Thyatira, a worshiper of God, listened,
and the Lord opened her heart to pay attention
to what Paul was saying.
After she and her household had been baptized,
she offered us an invitation,
"If you consider me a believer in the Lord,
come and stay at my home," and she prevailed on us.

-- Acts 16:11-15

From the very day of Pentecost the Church has celebrated and administered holy Baptism. Indeed St. Peter declares to the crowd astounded by his preaching: "Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit." The apostles and their collaborators offer Baptism to anyone who believed in Jesus: Jews, the God-fearing, pagans. Always, Baptism is seen as connected with faith: "Believe in the Lord Jesus, and you will be saved, you and your household," St. Paul declared to his jailer in Philippi. And the narrative continues, the jailer "was baptized at once, with all his family."

-- CCC 1226

The practice of infant Baptism is an immemorial tradition of the Church. There is explicit testimony to this practice from the second century on, and it is quite possible that, from the beginning of the apostolic preaching, when whole "households" received baptism, infants may also have been baptized.

-- CCC 1252