It seems to me, the moment that faith to do miracles arises is similar to that in which the faith unto salvation arises. Although not strictly necessary in the case of the miraculous (remember the Centurion), for the most part, I think the impetus of God is required for faith to distill. But also like that salvation moment, the final disposition of faith must come through us, not God. We believe, God does not believe for us, even though his instigation is what inspires it. Truly, there is nothing irresistible about the grace that stirs true faith into being.
Now there is a charismatic gift of faith through which faith is clearly inspired by God in the individual for the benefit of the body. That occurs for a specific purpose at a particular time--it is not ongoing, which is according to the intrinsic nature of a manifestation (phanerosis) of the Spirit. Yet, even this inspiration, like anything else the Spirit inspires, is quenchable. We are not puppets in the hand of God, after all, that would insult the one in whose image we are made.
When the breath of God is exhaled across the face of our inner person a moment arises--a moment which awakens faith and calls us to possibilities of moving as the hand of God in the miraculous. That stirring of the Spirit is a grace-filled invitation to believe and move with God. It's that tap on the shoulder we need to get beyond ourselves and get on board with God and do the miraculous.