"Very nice. I see what McGonagall meant... you really are a natural. I'm just going to teach you the rules this evening, then you'll be joining team practice three times a week."
-- Oliver Wood (PS10)
September 19, 1991 — Harry brings his new Nimbus 2000 broom to the Quidditch pitch as 7 pm. While waiting for Gyffindor Quidditch Captain Oliver Wood to show up, Harry flies around the goal posts, reveling in the responsiveness of the broom. When Wood arrives, he complements Harry’s flying, then shows him the Quidditch pitch and the equipment, including the elusive Golden Snitch (PS10).
The new broom and the first Quidditch practice happen "about a week" after the first flying lesson:
Hermione was now refusing to speak to Harry and Ron, but she was such a bossy know-it-all that they saw this as an added bonus. All they really wanted now was a way of getting back at Malfoy, and to their great delight, just such a thing arrived in the mail about a week later (PS10).
The first flying lesson was on Wednesday, September 12, so this event happened sometime around the middle of the following week, which would be around September 19.