Back in the first chapter (p. 14), Dulles indicated that he was assuming the question of the origins of faith. In other words, he takes as given the remote past of the faith, and the successive layers of covenants between God and man - i.e., Adam both before and after the Fall, Noah, Abraham, Moses; then the successive renewal of the Mosaic covenant down to the Incarnation. This allows him to look at the big-enough topic "what is revelation" without having to parse repeatedly the even-bigger question "what is the relationship between revelation and faith." That would be too difficult a project.
But Tom and Dennis are raising the question, so let's step out of the book for a moment to consider that more closely.
There is a traditional apologetic answer to this question -- Augustine's masterpiece "On the City of God" is an excellent example -- which I think is still really the clearest and fullest one. It is the one Dulles is in fact assuming. It boils down to a fairly simple theology of the Fall, its corrosive effects on various created natures, and their redemption in Christ.
(1) Adam sinned by an act of disobedience. Thereby he lost the gift of the possibility of not sinning. We his children, therefore, inherit a corrupt nature, carrying the not-possibility of not-sinning. We call this concupiscence. It affects our will (we sin) and our intellect (we can't grasp God properly).
(2) He did not, however, lose either his status as a creature (God still loves him and us in the same way) or his purpose as a creature ("to know, love, and serve God in this life, and to be with Him eternally in the next").
Moreover, the goodness of creation is still good. It still reflects the goodness of God.
(3) So, despite concupiscence, our purpose of loving God still draws us to those aspects of His creation that fulfill, even if only partially, that purpose. These we call "natural virtues," such as the "Big Four:" prudence, temperance, justice, fortitude. We know these are good from our experience, and from any reasonable analysis of the outcomes of actions based on these versus the alternatives.
God uses these, then, to call us to him. This is the underlying, "historical," layer of faith: a choice to respond with prudence, temperance, justice, and fortitude to the goodness of creation.
(4) Those who make this choice are therefore open to a further step in "knowing, loving, and serving God in this life, and being with Him eternally in the next." Outside of the specific revelation to Israel, there were and are naturally virtuous people, even lacking any clear knowledge of God's person: Augustine and other apologists point to some of the early patriarchs, philosophers like Plato or Cato the Elder, statesmen like Cincinnatus, lawgivers like Solon, etc. And of course ordinary people too, about whom we may know nothing.
Within the specific revelation to Israel, knowledge of God slowly became more clear: rooted in this "natural revelation" but gradually adding more and more specificity about who God is as Father, and what He desires from us as His children. This reaches its fullest point in the Incarnation. Christ leaves this fullness in the Church He wills, etc.
(5) Like every good thing from God, faith is, therefore, first and foremost a gift. In the general sense, it is the invitation to respond with natural -- and, eventually, supernatural -- virtue to the goodness of creation, and of the gift of being itself. We are free to respond positively or negatively. In the specific sense, it is the grace of God in me, against the impulse of concupiscence, strengthening and guiding my intellect and will, so that I may choose more positively than negatively. But even under the action of grace, I remain free to believe or reject. (This is quite a separate mystery, btw.)
As gift, faith is prior to revelation. It can be received even by infants, and so we not only practice but strongly encourage infant baptism. But, in another sense, revelation leads us to faith, which is why adult conversion (and baptism) is always possible.