So, I finally began my rereading of BLEACH. Inevitably, these panels pop up.
Which I assume to occur on the same day and not two different Fridays, as well as the rest of the chapter.
Now, if we take that 2001 is the modern year when Chapter 1 begins - then this occurs sometime during May 2001 (by Uryuu’s helpful comment later on, and timeline deductions).
Which gives us these possible dates: May 4th, May 11th, May 18th, or May 25th of when they met.
If we remember Chapter 2, Rukia shows up at Ichigo’s school the very next day - on a Saturday. It slots right into Japan’s school schedules where their only day offs of the week is Sunday.
Now back to the first panel for another clue - the cycle phase of the moon. It’s a waning crescent.
May 18th, 2001 aligns perfectly on both of those accounts. (Taken from here.)
In Chapter 35, Ishida Uryuu further supports it about when they did meet being the same day:
On the night of eighteenth of May in 2001 (mid-May), the tale of destiny begins.
 BLEACH’s anime make it seem it occurs over two days for the entirety of the chapter which isn’t the case. Unfortunately, it messes up the timeline a bit by making the next morning happen after the business with Dead Girl & her flowers. Yeah. Which would have moved their meeting to somewhere that isn’t mid-May as Uryuu says.  Any sense is taken out by the anime replacing the moon for an aesthetic full moon - which make it fall between May 6th - 8th and not a Friday, so. It’s a no go on their part to figure out dates.
NOW ON VIEW in the Contemporary Art Galleries— El Morois part of Omar Victor Diop’s ‘Project Diaspora,’ a series of photographic self-portraits based on historical works of art depicting notable men of African descent. This photograph is modeled on A Moroccan Man (1913), a watercolor by the Catalan painter José Tapiró y Baró. Here, Diop adopts the pose and garb of the original subject, but adds touches of modern life via the vibrant textiles and soccer ball. In discussing contemporary soccer players and the man represented in the original work, Diop said that he chose to reference soccer to “show the duality of living a life of glory and recognition,” while also facing the challenges of being “other.”
Diop began making these works during a four-month residency in Spain, a time during which he experienced a sense of cultural displacement that is mirrored in broader terms by the series itself. Utilizing source material likely drawn from The Image of the Black in Western Art,a research project, photographic archive, and multi-volume book series founded in 1960 by art patron Dominique de Menil, ‘Project Diaspora’ looks particularly at European history from the 15th to the 19th centuries, a period of intense interaction between Africa and the rest of the world.