I think it is important to note that in the pericopé that is our Gospel reading for this Sunday, it is "Bartimaeus, a blind man, the son of Timaeus" who sees from the get-go, even before Christ heals him. Attend to how Bartimaeus calls out to the Lord: "Jesus, son of David, have pity on me." With these words the blind man gives evidence that he sees who Jesus is- the Messiah. Notice that, while the Lord grants Bartimaeus his request (to see), He tells the son of Timaeus that his faith has saved him.
"Faith" and "saved" are two very important words in this passage. What these words mean are crucial for Christianity. The word "saved" in this passage in a translation of the Greek verb that transliterates as sesoken (literally "has saved"), which is derived from the verb sōzō, which has a range of meaning from being made well to being delivered from peril. There is no need to reduce what our Lord says to only one meaning.
As for "faith," the Greek noun employed in this passage is pistis. Pistis is (too) often viewed as the opposite of gnosis, or "knowledge." Such a false opposition gives rise to the persistent temptation to divorce faith from reason, which separation is the sad legacy of the Protestant revolt. As Von Balthasar explained in the first volume of his theological aesthetics, The Glory of the Lord:
The contrast between 'pistics' and 'gnostics' is basically that between, on the one hand, the Christian who, by 'bare faith'..., relates in a purely external manner to the content of faith (who, therefore, does not progress beyond a faith based solely on authority, which primarily means obedience to the ecclesial kerygma), and, on the other hand, the Christian who energetically strives to appropriate interiorly what he believes and, in so doing, sees the essential content of faith unfold before his vision..." (137)
We know from Christ Himself that a person can only know Him as Messiah and/or Lord by faith, which comes by way of revelation, an unveiling (Matt 16:17), or, in the words of Luigi Giussani: an event (i.e., something that happens to you) that becomes an encounter. Faith, by its true nature, as St Anselm of Canterbury noted long ago, seeks understanding. In other words, faith strives to know. Hence, faith and reason work together to bring us to the knowledge of the Truth.
Now, I readily grant that the above is an oversimplified explanation of the dynamic at work in faith, but I hope I give what amounts to a useful sketch. However, in Jesus' healing of Bartimaeus we have a perfect, and very dramatic, example of how pistis (i.e., true faith) leads to, or tends towards, gnosis (true knowledge).
Our first reading, taken from the book of the prophet Jeremiah, is about God doing for His people what Christ did for Bartimaeus. In our reading from the Letter to the Hebrews, the inspired author seeks to explain something of just how God does this in and through Jesus Christ, the great and true High Priest. So, with the psalmist and with Bartimaeus, let us rejoice, singing: "The Lord has done great things for us; we are filled with joy."