wrong-
john 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
if you have to be baptized to be saved it would have been included here. and other places.
It came from the Greek baptisma or baptismos, which meant to dip or to immerse. When John the Baptist started calling for people to repent and be baptized, there was no confusion about the meaning. Anyone who went to John the Baptist was literally immersed into water, and that was baptism.
So, to complete the thinking here Salvation is from Jesus Christ whose own words instituted Baptism. So, Baptism comes from Jesus and is required by Jesus to be Born again, "Amen, amen, I say to you, no one can enter the kingdom of God without being born of water and Spirit." Jn 3:5.