Actually Doolittle had already done it off the coast of Norfolk.
During the mission they had a good wind and with the carrier’s added speed you can see them just about lifting into the air well before reaching the end of the runway.
They at first appear to be barely moving but they are going into something like 80mph winds One made it even tho he forgot to set his flaps.
The take off’s can be seen on YouTube. They were filmed from a US Navy destroyer, I think.