Ditto on launchers
Lots of work was already underway on heavy left launchers -- I think the Saturn I design also preceedes the "Man on the Moon" speech.
In the mid-50s it wasn't clear yet that hydrogen bombs could be made small, and so we had studies underway for humongous ICBMs. Those turned out not to be needed, but the Saturn V engines drew very directly on research that was already being done for potential missile applications.