The Asst. DC of the 4th was General Teddy Roosevelt, Jr. He badgered the Div. Commander until he finally got permission to land in the first wave, the only general officer to do so.
And it's a good thing he did. After reconnoitering where they were, Teddy made the on the spot decision, "we'll start the war from right here!" He rejected any suggestion to re-embark and land again to the north. He was awarded the Medal of Honor.
Just re-watched The Longest Day and for my two cents, General Norman Daniel "Dutch" Cota, Sr., who landed on Omaha Beach in the 2nd wave, was by all accounts the major reason the invasion there succeeded. His above the call of duty leadership and fighting spirit on Omaha and the battle inland are the stuff of legend. He should have been awarded the Medal of Honor for his actions.
Which, by the way, would have made him the holder of all the US Army combat medals for bravery because he has already been awarded the Distinguished Service Cross, the Silver Star with oak leaf cluster, the Bronze Star with oak leaf cluster and the Purple Heart.