There is two known ways to access Bottom of the Well early, both of which requires the use of triple slash.
This method requires it to be day as you use a Cucco combined with Triple Slash Clip which allows you to get out of bounds.
There is multiple acute angles in Kakariko Village that allows you to enter BotW with the use of a Cucco. The most popular one being located to the left of the tunnel, coming from the graveyard. Another less popular one is located next to the back entrance of the Potion Shop.
The boulder that blocks the BotW entrance is not present during night, making it possible to enter with the use of Triple Slash Dive.
By exiting through the crawlspace next to the fountain from the main room and opening the door before the camera adjusts, you can unload the main room of the dungeon. As of now this is completely useless, except it can save you from collecting all the keys.
By throwing the boomerang so that it enters the coffin and hits the key inside of it as it returns to you, you can skip opening the coffin by lighting the torch.