When Jesus arrived of Cana of Galilee, he encountered a nobleman with a sick son. The nobleman likely knew that Jesus can do extraordinary things (note that Cana is also the place where Jesus turned water into wine, not to mention how the Galileans were away of Jesus's feats as stated in 4:45), so he requested Jesus to heal the son.
Jesus's first comment is a bit peculiar. He proclaimed how the Galileans would not believe "unless [they] see signs and wonders" (4:48). In other words, Jesus knew that the Galileans are over-reliant on Jesus doing the signs in their sight in order for them to trust Jesus. Such overreliance is demonstrated when the nobleman asks for Jesus to "come down" and do healing (4:47, 49). The problem of over-relying on signs and wonders is that it could lead people to think that if there are no signs and wonders, then Jesus would not be there (when in reality, Jesus works even if he doesn't do these miracles). And the problem of over-relying on Jesus's physical presence is that it could lead people to think that if Jesus is not there in person, then he could not work (when in reality, Jesus works behind the scenes).
Thus, in response to the request for healing, Jesus told the nobleman to "go [his] way" because "[his] son lives" (4:50). The healing method is meant to counter over-reliance on seeing signs from Jesus because the nobleman has to take Jesus's word for it and just move on. But even with incomplete information, the nobleman knew that the significance of Jesus is just too important for the claim to be discarded, so the nobleman trusted Jesus -- in faith.
Even today, walking with Jesus is often a walk of faith and trust on Jesus based on what we know Jesus has done (not just 2000 years ago, but also in us).