Firstly, thanks for bringing up this topic, its one of the main points of contention among Indian Ambedkarite Buddhists who take the book ‘Buddha and His Dhamma’ as a perfect Gospel, free from Brahmanical influences (which they take to be the doctrines of karma, rebirth and deva realms).
AFAIK, Ambedkar was not satisfied with the traditional story of the Bodhisatta’s going forth as a result of the famous Four Sights, and was instead looking for a more grounded, historically and logically plausible explaination. The traditional account of him encountering illness, old age and death for the first time at the age of 29 and then sneaking out at night actually seems too far fetched, and isn’t supported by the EBTs too:
“Some time later, while still black-haired, blessed with youth, in the prime of life—though my mother and father wished otherwise, weeping with tearful faces—I shaved off my hair and beard, dressed in ocher robes, and went forth from the lay life to homelessness.”
- MN 36
So, no midnight sneaking out while everyone was sleeping, more like an official Going Forth/Pabbaja in the midst of his family. So Ambedkar’s (or Kosambi’s ) version seems to have at least some historical basis.
A similar thread where this account was discussed :
“Straight ahead, your majesty,
by the foothills of the Himalayas,
is a country consummate
in energy & wealth,
inhabited by Kosalans:
Solar by clan,
Sakyans by birth.
From that lineage I have gone forth…”
- Pabbajā sutta (Snp 3.1)
“King Pasenadi of Kosala knows that the ascetic Gotama has gone forth from the neighboring clan of the Sakyans. And the Sakyans are his vassals. The Sakyans show deference to King Pasenadi by bowing down, rising up, greeting him with joined palms, and observing proper etiquette for him…”
- Aggañña sutta (DN 27)