A verb for a more precise way of showing a puzzle?

I would suggest either view or think about:

One way to view that puzzle is to ask whether life has any purpose at all.

as in:

view

VERB

2. [with object and adverbial] Regard in a particular light or with a particular attitude.
   ‘farmers are viewing the rise in rabbit numbers with concern’

or

One way to think about that puzzle is to ask whether life has any purpose at all.

as in:

think

VERB

2.4 (think of/about) Consider the possibility or advantages of (a course of action)
‘he was thinking of becoming a zoologist’

There's also consider:

consider

VERB

[WITH OBJECT]

2. Look attentively at.
   ‘the old man considered his granddaughter thoughtfully’

Hope this helps.

In the context of your sentence the word "consider" would work well. In your example the you have already 'presented' a puzzle, (or 'framed a complex question' perhaps? )

Your circumstance suggests that the 'puzzle' is one that might not have a clear resolution however one which other truths/concepts might be made clear in it's contemplation

One way to consider that puzzle is to ask whether life has any purpose at all

address is another possibility.

One way to address that puzzle is to ask whether life has any purpose at all

definitions:

https://en.oxforddictionaries.com/definition/consider (consider) Think carefully about (something), typically before making a decision.

https://en.oxforddictionaries.com/definition/contemplate (contemplate) Think carefully about (something), typically before making a decision.

or the third definition of the verb form of "address"

https://en.oxforddictionaries.com/definition/address 3)Think about and begin to deal with (an issue or problem)

Note: With a different example question, common terms used with puzzle are "unravel" and "solve" . I don't think one can truly "unravel" the question of whether life has any purpose, and given it's age-old and philosophical nature, it is unlikely to be 'solved'. In some ways this is a less typical way of using the word 'puzzle' however the alternative words to 'puzzle' might seem 'stuffy' or overly formal for your target audience.

How about approach?

Life in this world seem to be a puzzle. One way to approach that puzzle is to ask whether life has any purpose at all.

Here, it means you ask the question to get a bit closer towards the puzzle and its solution.

Merriam-Webster

1

a : to draw closer to : approach a destination

b : to come very near to : to be almost the same as

"… its mathematics approaches mysticism. — Theodore Sturgeon"

"...as the quantity x approaches zero..."

2

a : to make advances to especially in order to create a desired result

"...was approached by several Broadway producers"

b : to take preliminary steps toward accomplishment or full knowledge or experience of

"Try to approach the subject with an open mind."

One way to elucidate/unravel/decipher/crack that puzzle is to ask whether life has any purpose at all.

ODO:

elucidate VERB

[WITH OBJECT]
Make (something) clear; explain. ‘work such as theirs will help to elucidate this matter’

‘But this same light is a photographer's gift, elucidating the complexities and contrasts of the country.’

unravel VERB

[WITH OBJECT]
2 Investigate and solve or explain (something complicated or puzzling)

‘It's got structure, but it's like unravelling a puzzle.’

decipher VERB

[WITH OBJECT]
1.1 Succeed in understanding, interpreting, or identifying (something)

‘Have you ever tried deciphering a doctor's prescription that looks like some sort of secret code out of World War II?’

crack VERB

3 informal [with object] Find a solution to; decipher or interpret.

‘We've now discovered another challenge that may be harder to crack.’