“As soon as a man can say that he does believe, or is willing to believe, we emphatically assure him that he is on his way.” (Page 47, Big Book)
Once I believe that God can restore me to sanity, I can take action to switch my life onto the basis of a 100% reliance on God.
Until that point, the best I can do is be willing to believe.
Belief, itself, is not subject to will. Once simply cannot will a belief, because belief in an assertion is based solely on the availability of sufficient evidence. If there is evidence, I will believe. If there is not, I will not, regardless of however much I want to believe or I am under serious threat because I do not believe. One cannot ‘beat’ belief into a person.
What on earth does willingness to believe mean, therefore?
Willingness always concerns action, so willingness to believe means willingness to acquire sufficient evidence to belief.
What evidence?
As with anything, one can learn from those one trusts (‘authorities’), one can gather evidence oneself, and one can apply reason to pertinent propositions and evidence.
Being willing to believe, practically speaking, therefore means listening to others’ experiences and reading pertinent matter, taking actions to have metaphysical experiences (i.e. the Steps and their various components), and using reason (sometimes with others’ help) to arrive at conclusions.