I'm kinda unclear on it, here.
Did it occur before or after mortal races sprang into existence? (we know the Prime material plane and even Oerth existed since part of the war took place on the Plains of Pesh)
Or did it simply occur in an antediluvian era when mortal races existed, but few or none known by today's standards?
I ask this because I have contemplated on the fact that many prime worlds had their last great ice age at around the same time. This likely means that they had their Triassic age, Carboniferous, etc. at around the same time as well.
The only explanation for this is that the multiverse was affected by the makeup of the Inner Planes at the time-- e.g. during the Permian Triassic period, Magma and Fire predominated. I think such explanations could make for interesting history between the Inner powers (for instance, I could picture Yanny and Chan making a temporary treaty while they return fire and water to an equilibrium, seeing as how Yanny derives more power from Paraelemental Ice than he does from Smoke, and Chan's sub-portfolios are downright hostile to smoke), but I'd need to know when the Law/Chaos war takes place in the grand scheme of this beforehand (before it breaks out, I can't picture such disastrous imbalances occuring between the elements-- the Vaati Empire would seek to maintain an equilibrium between the four elements, or at least between fire and water.)
Both before and after. It began before the birth of mortal races, but continued into the era of mortals. Remember that tanar'ri were involved in the war (Miska the Wolf-Spider was one, for example) and the first tanar'ri were created from mortal souls.
"As mortal life appeared and their souls came to the Abyss, the Queen of Chaos was among the first to cultivate and nurture this new breed of demon - the tanar'ri." - Dragon #357.
That's probably right.
"Many thousands of years ago, long before the rise of human civilization, two ancient powers struggled to determine the fate of the still-forming multiverse. On one side was a primal being called the Queen of Chaos, a tentacled horror from an age before ages. Against her stood the rigid legions of the Wind Dukes of Aaqa, the most cultured of the elemental lords who ruled before the birth of the living races, and who yet controlled an empire that spanned worlds." - Dungeon #124.
"In ages long past, before the rise of elves, dwarves, or humans, the legendary Wind Dukes of Aaqa ruled a vast empire, bringing Law and elemental magic to many barbaric worlds." - Dungeon #129.
So at least at the beginning of the war, modern races hadn't yet "risen." That doesn't mean they couldn't have been around by the end of the war, or that they didn't exist at all early on, but it was clearly a long time ago.
There's a wrinkle to this. Inevitables were involved in the war, as servants to the vaati.
"Air and lightning powered their magic, and their ties to the Plane of Elemental Air were very strong. In time, they mastered other elements as well, and as they grew more and more powerful, dozens of other elemental and lawful races swore fealty to them, from the lofty djinn and the proud salamanders to the least of the mud sorcerer cults and the inevitables, servants of the Wind Dukes. At its peak, the empire of the Wind Dukes comprised most of the elemental planes ,from the oceanic palaces of the marid to the City of Brass." - Dungeon #129, p. 40.
Okay, but Dragon #341 says this about the origins of the inevitables. "By the standards of the eons-old multiverse, the rise of the inevitables is a relatively recent occurrence. Some historical texts (most notably Gantrhos the Elder's Accounting of the Realms Beyond and Hannak Lathar's Verses of the Blood War) trace their emergence to 10,000 years ago."
If we're to assume these in-character texts are correct, the Battle of Pesh must have taken place no more than 10,000 years ago, which is after the elven Crown Wars on Toril, though before the earliest known human civilizations on that world. Shekelor lived in Sigil 10,000 years ago, though I'm not sure we know for sure that Shekelor was human.
Personally, I'd place the Battle of Pesh well before then, and assume there were some inevitables around long before Ganthros and Lanthar's texts imply (though they may not have been as common as they are today). A million years ago wouldn't be too far in the past in my opinion.
And there's some evidence it was more than a million years ago. The tanar'ri lord Turaglas was born a million years ago according to Dragon #312. He could have been created before the Battle of Pesh, but the existence of tanar'ri places him at the very least in the latter era of the war. The timeline in Hellbound: The Blood War has the demons and devils figuring out how to make more fiends from mortal souls very late in the history of the war, so the tanar'ri proper wouldn't have been created until then. First Demogorgon, then Turaglas (born directly from the Abyss rather than created, but Demogorgon was the first tanar'ri) and Miska later on, and only after that could the Battle of Pesh have happened.