A few more thoughts about context for John 9:39. In this passage, the Pharisees claim to be the ones who see, who know exactly how to judge Jesus, but they judge him wrongly. The blind man is a little more humble:
24 Ἐφώνησαν οὖν τὸν ἄνθρωπον ἐκ δευτέρου ὃς ἦν τυφλὸς καὶ εἶπαν αὐτῷ· Δὸς δόξαν τῷ θεῷ· ἡμεῖς οἴδαμεν ὅτι [z]οὗτος ὁ ἄνθρωπος ἁμαρτωλός ἐστιν. 25 ἀπεκρίθη οὖν ἐκεῖνος· Εἰ ἁμαρτωλός ἐστιν οὐκ οἶδα· ἓν οἶδα ὅτι τυφλὸς ὢν ἄρτι βλέπω.
The blind man does not claim to know if Jesus is a sinner, all he knows is that he was born blind and now he sees. But the Pharisees couldn't explain the miracle, they first tried to deny that the man was ever blind, then they questioned him, trying to figure it out, but never admitting the possibility that Jesus might be sent by God.
The Pharisees then accuse him of being a disciple of Jesus rather than of Moses, and now the Pharisees admit to not knowing one thing - they do not know where Jesus came from:
28 ἐλοιδόρησαν αὐτὸν καὶ εἶπον· Σὺ μαθητὴς εἶ ἐκείνου, ἡμεῖς δὲ τοῦ Μωϋσέως ἐσμὲν μαθηταί· 29 ἡμεῖς οἴδαμεν ὅτι Μωϋσεῖ λελάληκεν ὁ θεός, τοῦτον δὲ οὐκ οἴδαμεν πόθεν ἐστίν.
The blind man then accurately interprets the meaning of what has happened, but all the Pharisees can do is dismiss him as a person, saying that he was born in sin and has nothing to teach them, and sending him away:
30 ἀπεκρίθη ὁ ἄνθρωπος καὶ εἶπεν αὐτοῖς· Ἐν τούτῳ γὰρ τὸ θαυμαστόν ἐστιν ὅτι ὑμεῖς οὐκ οἴδατε πόθεν ἐστίν, καὶ ἤνοιξέν μου τοὺς ὀφθαλμούς. 31 οἴδαμεν ὅτι ἁμαρτωλῶν ὁ θεὸς οὐκ ἀκούει, ἀλλ’ ἐάν τις θεοσεβὴς ᾖ καὶ τὸ θέλημα αὐτοῦ ποιῇ τούτου ἀκούει. 32 ἐκ τοῦ αἰῶνος οὐκ ἠκούσθη ὅτι ἠνέῳξέν τις ὀφθαλμοὺς τυφλοῦ γεγεννημένου· 33 εἰ μὴ ἦν οὗτος παρὰ θεοῦ, οὐκ ἠδύνατο ποιεῖν οὐδέν. 34 ἀπεκρίθησαν καὶ εἶπαν αὐτῷ· Ἐν ἁμαρτίαις σὺ ἐγεννήθης ὅλος, καὶ σὺ διδάσκεις ἡμᾶς; καὶ ἐξέβαλον αὐτὸν ἔξω.
So the passage is all about who can see and who cannot see. The man born blind and made to see is contrasted with the blindness of the Pharisees, who insist more and more loudly that they are the ones who can see, and shut their eyes to Jesus.
Now we come to the verse in question, verse 39:
39 καὶ εἶπεν ὁ Ἰησοῦς· Εἰς κρίμα ἐγὼ εἰς τὸν κόσμον τοῦτον ἦλθον, ἵνα οἱ μὴ βλέποντες βλέπωσιν καὶ οἱ βλέποντες τυφλοὶ γένωνται.
We often think of judgement as the final judgement, but let's consider the senses of the word in Louw and Nida, as Iver has pointed out:
f judgment 30.110
e lawsuit 56.2
a legal decision 56.20
b authority to judge 56.22
c verdict 56.24
d condemnation 56.30
Iver says that in the above verse, the preposition εἰς cannot refer to purpose. I do not yet understand why that is true. To me, the most natural reading is that the judgement is not the final judgement, but judging between those who claim to see by their own knowledge and understanding and those who come to see, not by their own power, but by the transformative power of Jesus.
And that seems to be the way the Pharisees understood what Jesus said:
40 ἤκουσαν ἐκ τῶν Φαρισαίων ταῦτα οἱ μετ’ αὐτοῦ ὄντες, καὶ εἶπον αὐτῷ· Μὴ καὶ ἡμεῖς τυφλοί ἐσμεν; 41 εἶπεν αὐτοῖς ὁ Ἰησοῦς· Εἰ τυφλοὶ ἦτε, οὐκ ἂν εἴχετε ἁμαρτίαν· νῦν δὲ λέγετε ὅτι Βλέπομεν· ἡ ἁμαρτία ὑμῶν μένει.
In this last verse, note that Jesus does not say, "now that you say you see, you are condemned to the final judgement". He says "now that you say you see, your guilt remains". Jesus renders a verdict here, but it is not the last judgement.