I am aware that "gamble" means to risk or bet, bur I am puzzled by "gamble one's way." here it goes in context: "We are going to gamble our way to belief in God." Maybe the speaker left out "on" like "gamble on our wat," I am not sure. Tell me please what you think of this.
VERB one's way to GOAL is a fixed English construction (in fact it is one of the 'parade' examples analyzed by Construction Grammar) with the primary sense
proceed to GOAL by VERBing—the action designated by VERB is the means or method of achieving GOAL
Go thrust him out at gates and let him smell his way to Dover—said by Goneril in Shakespeare's King Lear after her husband has put out Gloucester's eyes; since Gloucester can no longer see he will have to discern his route by smell.
This Arkansas football player danced his way to an NYU scholarship—a news story about a high school athlete who achieved a scholarship at a prestigious New York university through his study of dance.
The construction is also employed in a 'non-causative' sense
proceed to GOAL while VERBing—the action designated by VERB accompanies progress toward GOAL
J. L. cheerfully whistled his way to the elevator. No sense in worrying about things that hadn't happened yet. —Cara Saylor Polk, Code Koral
In your quotation the first, causative sense is probably what is meant: it seems to echo Pascal's wager and Samuel Butler's comment on Job 19:25, I know that my Redeemer liveth:
What is faith but a kind of betting or speculation after all? It should be “I bet that my Redeemer liveth.”
That is, belief in God can only be achieved by making a concrete commitment to belief—a ‘bet’ which accepts the risk of losing.