The best time to start completing puzzles to reach your Weekly Challenge's "Complete X Puzzles from this week" goal is between the start and end times of the event, and not the calendar week.

Each Weekly Challenge starts on Wednesday, 7 P.M PT, and ends on Tuesday, 7 P.M PT. This means that Puzzles published from Wednesday 7 P.M PT until Monday, 7 P.M PT (Tuesday's Puzzle) will be counted for that specific week.