The example in your question suggests you're trying to describe the act of beginning or preparing to make an attempt to solve the puzzle. One good word for this is approach:
One way to approach that puzzle is to ask whether life has any purpose at all.
Another phrase with similar meaning is crack into, alluding to the process of cracking open the shell of a nut (the puzzle) in order to reach its contents (the solution). Note this is a different term from the usage of crack suggested in alwayslearning's answer - by cracking into a puzzle you're beginning the attempt to solve it, while cracking the puzzle is the act of completing a solution.
Your example also demonstrates solving a puzzle by breaking it (down) into smaller, more specific puzzles. With some slight rewording, this term fits the example pretty well:
One way to break that puzzle down is to ask whether life has any purpose at all.
The word simplify offers a similar fit in this sense, though in this particular case such grand puzzles are hardly "simple".
Along the same line of thought, you might consider digest, as you're describing the act of converting a large object into more basic components for easier manipulation. Digest is often used to describe the act of thinking about something thoroughly in order to understand it, especially if it's not easy to do so. The metaphor, of course, is the chemical processes of the stomach and intestines as they break food (complex problems) down into easily-absorbed nutrients (simple constituent problems) and then absorb (solve) them.