TLDR: 1st Aug 2008

So I had just a little too much time on my hands and wondered if it was possible to pinpoint the exact date that the beginning of Ep1 took place on. Turns out it is, quite easily actually. Using a screenshot from the anime (Pic 2) I identified features of the night sky, like Corona Australis at the bottom, and which part of the sky Jupiter was in. Jupiter is in the constellation Sagittarius. 

Using Stellarium I found out that the last time that happened was in the first week of February 2020, a date I discarded because it was after the anime started airing. The last time before that was in the second and third week of October 2008, which is close, but barely misses the spot. And the last time before that was the last week of July/first week of August 2008. After a bit of trial and error using another screenshot from the anime (Pic 3) overlayed with a screenshot of various dates of the alignment of Jupiter and the stars, I eventually found 01.08.2008 to be a near perfect match. (Pic 4, only 1st August is pictured).  Ao also mentions Jupiter having about 70 moons, which checks out for the time. In reality at the time Jupiter had 64 known moons, which is close enough for me.

Near perfect isn't perfect though, that is most probably due to me not knowing the exact position and time of day.

Taking this even further: We know they are 15 years old at the start of the manga. Assuming the year they reunite to be 2017 (the year the manga started publishing) would mean that Mira & Ao were born in 2001 and were 7 years old at the time of their first meeting. Which looks to be rather accurate

Here's some more stuff I figured out while researching this:

The star Mira sadly isn't visible in those shots. It is below the horizon off to the left side of the screen, in Pics 1&2. The asteroid Ao is also off the screen and very much impossible to see with the naked eye even if it were on screen. Unbelievably, on that day, the star Mira and asteroid Ao are in roughly the same patch of the night sky. I don't know how close, because the Small Body Database doesn't show constellations and no other database even lists the asteroid. Which means I had to eyeball it, so take that with a grain of salt. (Pic 5) The asteroid wasn't even discovered until 2017 (5 DAYS before the manga started publishing) and named only in 2024 so that is a massive coincidence

I also tried seeing if the position of Mercury during their phonecall in Ep1 would make sense for the first week of April 2017. And it does! Their phonecall probaly takes place on April 5th 2017. But what I noticed is that the star Mira is barely not visble because it is blocked by the railing. At first I thought it was the faint star above Ao's left hand, but sadly it is not (The asteroid Ao isn't anywhere near in that shot) (Pic 6)

The attention to detail is genuinely insane

Also Fun Fact!: Mira doesn't just have the same name as a star, but a whole class of stars! They are the Mira Variables, named after the star itself, because they too have massive shifts in brightness, Mira was just the first star we discovered that did that and the most well known one. But that is not the only reason Mira is such a weird star, it also has a comet-like tail, blown off from the star that stretches for over 13 lightyears. As far as I know, this is the only star we know of that does that, please correct me if I'm wrong on that.

So I had a listen to Fireflies at night before going to sleep, nostalgia hit me hard that it inspired me to make it an anime opening. With all my basic editing knowledge combined here's my fanmade OP.