The word Shakespeare first used was probably "mama" although sometimes this is not the first word a child says. There is no real record of it, so it is mostly guesswork. If you mean "Which words did...
We don't know for sure. It was written before 1602 and probably after 1599. It was probably performed shortly thereafter. That leaves a very narrow window as Shakespeare plays go.
It is hard to know in what order Shakespeare's plays were written, or whether he had coined some words in conversation before using them in a play. This question, like just about any question about...
Polonius has just asked Hamlet what he is reading. Of course what he wants Hamlet to say is the name of the book. But just to be irritating Hamlet responds "Words, words, words."