Certainly there is the analogy, however it fails to support the premise that this was literally required for all subsequently, for this would require all those who were subsequently born to undergo this immersion.
And it is very clear that in the NT baptism is not essential for effectual, penitent, heart-purifying, regenerating faith, which is counted for righteousness, but it is to be concomitant with it.
Acts 2:38 mentions “every one of you”.
Abraham was commended for his faith.... after he had left Haran, travelled hundreds of miles (the hard way), built at least three altars and offered sacrifices on them. He had to hear the word of God and keep it. His faith would have been incomplete without acting upon it.
The epistles were written to people that were already born again. They knew the method of conversion in detail. Therefore, they didn’t need the details again.