I came up with this challenge while playing around working on Pie_Snipers Two-Door Challenge. (https://nifflas.lpchip.nl/index.php?topic=6850.0) His is more difficult, because of a special caveat, which I will detail below.
I found it is indeed possible to get the Vault Ending by unlocking only one single locked door. (Other doors may be used as normal.)
No cheat or developer mode.
-The two door challenge restricts the player from entering the Village. This challenge does not!
Done.You might want to change the rules to ban the cheat code and developer mode. The latter in particular allows you to get the vault ending without unlocking any doors at all.
Since that obviously wasn't at all how you intended this challenge to be done, I also did it without both though. As expected, it's much easier than Pie_Sniper's challenge. All you really need to know is how to get the gold and silver trophies using a teleport bomb and a teleport gun respectively. With the ability to access the village through the trophy room's back entrance, obtaining them is a piece of cake.