According to Anne Somerset, “Between eleven o’clock and twelve noon on 17 November 1558, Elizabeth was formally proclaimed Queen outside the Palace of Westminister, and at various other points around the capital” (Somerset 58).
It would not be an understatement to say that that moment changed everything.
But I don't have time for a bulleted list to give you the specifics. Instead, I'll recommend a book that I'd love to read if I had the time: Shakespeare and Elizabeth: The Meeting of Two Myths. I've only glanced through the book, but I can tell that I'd love to curl up with this one for a good while. Hackett examines what has been done with the lives of Elizabeth and Shakespeare, with particular emphasis (at least early on) on how stories about the two of them meeting have evolved over the centuries.
Of course, that fits the world of Shakespeare and film very well. Shakespeare in Love and Doctor Who spring immediately to mind. For the latter of these, take a look at this rare clip from a 1965 episode that shows Elizabeth I and Shakespeare together! That's the sort of thing Hackett examines in this book.
Hackett, Helen. Shakespeare and Elizabeth: The Meeting of Two Myths. Princeton: Princeton University Press, 2009.
Somerset, Anne. Elizabeth I. New York: St. Martin’s Press, 1991.