NASA actually planned out what his first words were going to be in advance of the Moon landing, so the first words on the moon weren't his own creation, much as Presidental speeches aren't of their own creation. He had some writers who gave him a line to say (I'm not insinuating that the mission was staged btw, before anyone gets any ideas).
I read a book on it a while back.
Fun fact: The crew was originally going to call the Lunar Module the Charlie Brown and the Snoopy, but NASA wouldn't have it, so they named it the Colombia and the Eagle.
The crew actually continued to refer to the modules as the Charlie Brown and the Snoopy in passing conversation aboard the rocket, and only used the "Official" names in transmissions to NASA.