“Many Samaritans from that town believed in him because of the woman’s testimony, “He told me all that I ever did.” 40 So when the Samaritans came to him, they asked him to stay with them, and he stayed there two days. 41 And many more believed because of his word.42 They said to the woman, ‘It is no longer because of what you said that we believe, for we have heard for ourselves, and we know that this is indeed the Savior of the world.’” – John 4:39-42
This passage is the end of the story of the Woman at the Well. I would encourage you to go back and read the whole narrative.
Jesus had told this woman many true things about her life without her revealing anything to him. He shares the good news of salvation through him without judging her for having five husbands. She knew of him well through the prophets and he confirmed her curiousity about who he was.
This is just one amazing example of the the encounters Jesus had with every day people. How would you react if the person you had heard about through the prophets, the Savior of the world approached you and chatted with you about your life?
59 times, the Savior is referenced in the Bible, and the majority actually come from the Old Testament. So if people were listening to the religious leaders, they definitely knew about the promise of God to send a Savior.
The woman did what I would do, which is to share what she had witnessed with others! And so many came to belief because of this witness! And many more welcomed Jesus to stay with them so they could hear it for themselves. And indeed, many recognized Jesus as Savior.