An answer to this would be just as the following:
If you can "wake up in the morning with full energy, eat when you feel hungry, be able to pass the bowels when needed and sleep when the night falls and when you feel tired" - you would have understood.
One might say, "What are you talking about? aren't those what we do every day?"
We wake up in the morning thinking of yesterday, when someone said something unpleasant to us, something that should have been finished, how much did you pay for the meal in a restaurant where the waiter was rude (or nice, that you must come back), etc.
We eat thinking of work, the co-worker who we need to pay attention to because he might be doing something ulterior, the "for-loop" the fails from time to time, etc etc.
We sleep thinking of tomorrow or next week, our holiday plans, what to wear, "how humiliated I was, when that Jack pulled a trick on me trying to impress the girl I try to get a date with", etc etc.
So, what is the role belief? As mentioned, one doesn't need to believe in anything.
There is no form. It is not the incense you burn or the perfectly cut rose wood that you set up in your home that make you a Buddhist, or how much you argumentatively "win" in a conversation with others about life or how many temples you have visited, etc etc.
As time goes by, and when the understanding is obtained, you lose the sense of "self" and thus "you". You mentioned Western and so I would take the freedom on making a comment correspondingly - in western culture, the "I" is huge, the "form" is more important and the "steps" must be followed sequentially (science) and the "things" must be studied and proven by mathematics and seen under the microscope; this is the only barrier I have experienced when one is learning to walk the path towards Buddhism.
What I have learnt is:
Observing. Learn how to observe yourself and the nature. If one can do something that is truly beneficial to other beings and livelihood that is not based on "self", it would be a good first step attained.