Galileo saw Neptune on december 27th 1612
From Starry Night: at around 5:00 AM in the morning
December 27:
January 3 1613:
January 4 1613:
Amazingly, Neptune is being occulted by Jupiter !!!!!!!!! (Well, at least for someone living in Antwerp).
What is recorded is that he did look at Jupiter in the morning of the 27th....Perhaps not the following days..yet...
He did see Neptune..but didn't discover it as he would not have known it was a planet (Newton's laws were not known yet).
To see and to discover are two different things.