Knowledge is not necessarily a knowledge of information written in the Scriptures. One can know how to fight sin of, say, alcoholism, and this is not a bookish knowledge, but a one that comes from an experience of fighting this damaging passion.
Here also, we have a logical sequence of a) faith, b) virtue and c) knowledge. Take an analogy: a) Bjorn Borg conceives faith that he can win Wimbledon; b) he develops and strengthens this faith by training and gaining the virtues of a superstar tennis player; c) having entered the Wimbledon tournament he gradually sets himself on the victorious course until he wins also the final and knows, already by experience and not merely a dream or expectation, what it is to win the Wimbledon final.
Same in life of faith in Christ: a) a promiscuous woman had faith that her sins could be forgiven by Jesus Christ; b) she augments and develops this faith by a virtue of humility and daring of overcoming the public opinion and public shame, thus she becomes virtuous alongside with being faithful, for virtue is formed by practicing the faith; c) she is actually forgiven by Jesus Christ and she experiences this forgiveness, coming therefore to its experiential/existential knowledge, and this will imply knowledge of Jesus Christ's divinity, for only God can forgive immediately, as Jesus Christ did to her, having forgiven her authoritatively, Himself, without asking or praying to God, which was immediately noticed as scandalous by the expert-theologians, probably the Pharisees present there (Luke 7:47-50).
Now, the profligate woman could not know about divinity of Christ from any text of the Jewish Holy Scriptures, but she existentially experienced the forgiveness of her sins and saw with her own eyes that Jesus Christ did it with His own self-sovereign authority, and that was enough for her to conclude that He was God. Similarly, when holy apostles worked miracles among non-Jews, they came to knowledge of the power of Christ sometimes without even knowing about any Scriptures whatsoever.