Does the library have books from the beginning of time to the 16th century?
We have books about the beginning of time, i.e. the Bible, through the 16th century; but no, we do not have original manuscripts, etc., from those eras. Those are quite rare and housed in special libraries and private homes around the world.
The Library of Congress is the United States' foremost special library.
The Bodleian Library , in Great Britain, houses a vast array of special collections.