For what it is worth, Catholics are traditionally baptized very young (one of our Sacraments). Then, at about age 12 or 13, we go through Confirmation (another Sacrament). This is the reaffirmation of our Baptism. But we are never “re-baptized). As others have said, Baptism welcomes us into God’s family (on his terms) and we are God’s people from that point forth.
I was baptized as an infant, just went through the motions of confirmation at the age of 13. The Holy Spirit did not regenerate my heart until I was in my 30’s. It was after then that I got baptized legitimately.