It depends on what the puzzle is?
Is there one puzzle or many?
To which puzzle do you refer?
“Holding” all the pieces to any puzzle is only possible if the puzzle is smaller or somehow less complex than the holder of the pieces. And “holding” implies a kind of distinction between the puzzle and the holder, whereas if you are talking about the “ultimate” puzzle, distinctions between the puzzle and the holder disappear, and we ARE the puzzle, part of the puzzle.
By “the” puzzle, I could assume you mean the entirety, which I call the universe. It makes no sense, I think, to speak of holding all the pieces of the universe, or “knowing” “everything” about the universe, except to say poetically that we all are manifestation of the universe, and by being it, we hold the pieces to the puzzle.
Also, it may sound overly simple or playful if I said, “Science knows what is knowable at the time it is knowable.” i.e. I could play and say that the word “science” comes from either the noun form or the substantive participial form of the Latin verb “scire” – “to know”; thus, science, scientia, is, at its root, “knowing,” or “knowings,” or “knowledge.” In that sense, science knows all that is known. It would be a true statement, according to etymology; but it is quite playful.
Whatever pieces of the puzzle “science” does “hold,” you will never know except to the extent that you know science. – another playful statement.
What do you think of this TED lecture by Richard Dawkins, “The universe is queerer than we can suppose” (22 minutes. July 2005.)? – http://video.google.com/videoplay?docid=6308228560462155344#. It is one of my favorite TED talks. It addresses this question in an entertaining manner.
Before I give any further attention to your question I think I will wait for you to see the lecture and also rephrase your question or elaborate. You may be wanting to get into epistemology, and that will be a great big can of worms. We can do it when the time comes. Or you may mean, “Is the scientific method the only valid method of inquiry?” We will see.