"Peter said to them, “Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit. “For the promise is for you and your children and for all who are far off, as many as the Lord our God will call to Himself.”
Note that the gift of the Holy Spirit to the Jews and their descendants and gentiles followed Peter's exhortation to "repent and be baptized." To repent means you acknowledge you are moving in the wrong direction and change. Infants cannot do any of that.
Another Christian named Origen wrote in about 250 AD:
“The Church received from the apostles the tradition of giving baptism even to infants. The apostles, to whom were committed the secrets of the divine sacraments, knew there are in everyone innate strains of sin, which must be washed away through water and the Spirit”
In other words, Origen is arguing that even though infants haven’t personally sinned yet, they still are possessed of the sin nature.
Theology aside, though, he clearly says the apostles would even give baptism to infants.
The New Testament teaching by Paul that our children are set aside and holy in the eyes of God would not conflict with that. Nor would the teaching of Peter in Acts that the promise is for our children. Nor would the teaching that Lydia’s, the Jailer’s, and Cripus’ households were baptized conflict with the baptism of infants. Nor would Jesus own teaching who said about infants, “Let the little children come to me.”
So, I could go on and on with others in early church history who testify to infant baptism at the earliest stages of the church.
On the other hand, you don’t have to accept that explanation, and you can have your reasons for not accepting it. However, what you cannot say is that those who do teach it have made it up out of thin air.
They haven’t.
There is a basis in scripture and church history for the teaching of infant baptism.