I've not been able to find the specific date, at which these three were mortal. Does anyone know? Is it perhaps not specified? I know that they were slain around 1358 DR, but at this point they had already become gods.
Their birthdates are unknown
Adeptus has helpfully provided some notes establishing years before which Myrkul and Bhaal would have been born, but their years of birth are not established. As for their apotheosis...
The timeline is not perfect, but...
Here are some important events:
• -359 DR, the Year of Boiling Moats, was when Bane, Bhaal, and Myrkul brought low Borem of the Lake of Boiling Mud, one of the Seven Lost Gods, and brought his heart to Cormanthor.
• -357 DR, the Year of the Sycophants, is given in a 4E adventure as the date in which the Dead Three fought and sealed Maram of the Great Spear.
• 106 DR, the Year of the Adamantine Spiral, documents activities of crusaders serving the Church of Myrkul. By this point they have become deities.
This gives us a range of 463 years between their last documented sighting on Toril and the first documented act of followers of one of their religions. As Adeptus notes, Alaundo made prophecies some 31 years earlier regarding one of the Dead Three, though I don't think that's really indicative - it's a prophecy, by definition it can refer to something which has not yet occurred, such as Bhaal taking on the title "Lord of Murder."
It's reasonable to suggest that Jergal was still in power at the time of the fall of Netheril, and while this cannot be guaranteed (his worship was being divided, after all, and by mortals besides) it's a good ballpark. This would move the posts closer, to -339 DR and 75 DR as Adeptus has suggested, still a range of 414 years.
Can we narrow it down?
Well... yes and no. A formal date for the apotheosis is of course not available, but for some plausible dates, we can look to the Roll of Years, the record naming years to come based on prophetic (and often disturbing) visions experienced by Netherese seer Augathra the Mad. A few specific names leap out from roughly the right time period, and I will address these:
-336 DR: the Year of Dark Sunset
Shortly after the Fall of Netheril, a good time for a god whose following is encountering societal upheaval to make a change. Jergal closing out his time as Lord of the End of Everything may poetically seem a "dark sunset."
-330 DR: the Year of Empty Quests
The Dead Three quested to slay Jergal and claim his throne by force. Jergal, of course, surrendered it without a fight. Probably a weaker theory, but not unreasonable.
-323 DR: the Year of Unseen Doom
For all the adventuring the Dead Three did across Faerûn, their ultimate act of apotheosis took place in Jergal's hall, far from mortal eyes, and would have serious ramifications over the course of the next thousand years and change. A reasonable candidate for "unseen doom."
-286 DR: the Year of Foul Awakenings
Three new gods of evil taking the place of one who had grown tired of his role, seizing the mantles of tyranny, murder, and the dead - foul awakenings indeed.
The tale of the Dead Three indicates that seizing the essence of one of the Seven Lost Gods was the penultimate step before confronting the Lord of the End of Everything. It is likely that their apotheosis took place relatively soon after the Fall of Netheril, and so I would conjecture that -336 DR is the most probable year in which this took place.
Again, unfortunately, this is conjecture - we do not have fixed dates, and even things such as the link between Tharlagaunt Bale and Jergal arise from what is identified as a fan creation presented on a now-defunct site. As with many matters pertaining to the deific history of the Realms, it will ultimately remain something of a mystery.
I haven't found exact dates, but I have managed to narrow it down a little.
Myrkul Bey al-Kursi, the Crown Prince of Murghôm, was said to have lived in the time of Ancient Netheril. So, he was born sometime before -339 DR.
Bhaal was known as Tharlagaunt Bale, and was one of Jergal's chosen ones in -696 DR, being granted some of his power. Ed Greenwood's old site says he rose to godhood "in the centuries that followed the fall of Netheril".
We can assume that they had ascended before 75 DR, as the seer Alaundo delivered a prophecy about Bhaal in that year.
I haven't found any record of Bane's mortal life so far.
- They became gods sometime between -339 DR and 75 DR.
- Myrkul (Myrkul Bey al-Kursi) was born sometime before -339 DR.
- Bhaal (Tharlagaunt Bale) was born sometime before -696 DR.