Indeed, according to what is written in Pirkei DeRabbi Eliezer (Chapter 42), Judah jumped first: "Rabbi Akiva says, the Israelites were going towards the Sea of Reeds and were turning back, fearing that the waters might return upon them. And the tribe of Benjamin wanted to enter there, as it is said, 'There is Benjamin, the youngest, ruling them,' they were descending. The tribe of Judah began to stone them, as it is said, 'The princes of Judah their council.' And Nachshon jumped into the sea first and sanctified the great name before everyone. And by the dominion of the hand of the children of Judah, all of Israel followed them into the sea, as it is said (Psalms 114:2), 'Judah became His sanctuary, Israel His dominion'—of Judah."