Please explain whether one can know God in any other way than by faith.
Since Buddhism doesn't use the theistic model to describe the religious quest, I first have to ask for a definition of God. In this case that isn't given (it might be a good question for the future) so let me paraphrase the question. Can the deepest realization in Buddhism be known in any other way than faith?
The Buddha's own spiritual quest culminated in his realization of nirvana. The teachings that arose from that realization were pragmatic instructions to enable others to share that same realization. He insisted that nirvana is indescribable. Sometimes he alluded to it in a negative manner, "There is the unconditioned, the uncreated, the deathless." The underlying image in our texts is one of freedom and ultimate happiness, something truly worth knowing. Faith in Buddhism is thus; trust in the enlightenment of the Buddha and the willingness to implement his teachings in order to realize the goal of the spiritual life.
Faith is necessary because it gets you going but in itself it is insufficient. You still have to walk the talk. Eventually, if one has done one's spiritual homework, the Buddha's realization of nirvana becomes one's own and then faith changes to confidence. One has gone beyond faith to knowing.
The work involved in realizing the goal is described in various ways but most simply it involves human development in three areas - ethics, meditation and spiritual insight. Under ethics are included the commitment to live a virtuous life based on moral integrity and kindness and generosity to others. Within the category of meditation are included the training of the heart and mind so that we are free from destructive emotions and have the ability to dwell in inner states of calm and compassion. Finally, the third area of development, spiritual insight, involves the ability to be ever more mindful and aware of our inner world and in meditative stillness come to the deepest spiritual realization which is sometimes known as "the unshakeable deliverance of the heart."