Chapter 8 of John's Gospel finishes with:
57Then said the Jews unto him, Thou art not yet fifty years old, and hast thou seen Abraham?
58Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am.
59Then took they up stones to cast at him: but Jesus hid himself, and went out of the temple, going through the midst of them, and so passed by.
John 8:57-59 (KJV)
Chapter 9 of John's Gospel begins:
1And as Jesus passed by, he saw a man which was blind from his birth.
John 9:1 (KJV)
Two points:
There are no chapter divisions in the Greek.
The word 'Jesus' doesn't appear in the Greek text of John 9:1, as the Greek text is:
Καὶ and παράγων passing by εἶδεν he saw ἄνθρωπον a man
So, the text, without the chapter break and without the additional word inserted, reads:
8:58Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am.
8:59Then took they up stones to cast at him: but Jesus hid himself, and went out of the temple, going through the midst of them, and so passed by.
9:1And as he passed by, he saw a man which was blind from his birth.
The chapter division has caused a break in John's narrative that shouldn't be there. John's readers would have immediately recognised the continuance of person, place and time of the events John was recounting here.
So, the Greek text makes it abundantly clear that Jesus restoring the sight of the blind man happened immediately following the encounter with the Jews, and therefore on the same day.
Now, all of chapter 9 concerns the event surrounding the man whose sight Jesus restored.
At the end of Chapter 9 the Jews ask Jesus:
40... Are we blind also?
John 9:40 (KJV)
Then Chapter 10 begins with Jesus demonstrating the blindness of the Jews by relating to them a parable that they didn't understand:
6This parable spake Jesus unto them: but they understood not what things they were which he spake unto them.
John 10:6 (KJV)
Then immediately following Jesus' declaration, "I and my Father are one", John records this:
31Then the Jews took up stones again to stone him.
John 10:31 (KJV)
There is no doubt that the events depicted in Chapters 8, 9 and 10 occurred on the same day.