We could pick from the most basic equipment in charater creation (Starter gear only, nothing fancy,), and that could be on the first body we find or in a chest in the first room.

So in the equipment part of CC, I could choose to give my Warlock a simple robe (allowing me to replace the padded armour that is the default for Warlocks now with something more in keeping with my characters RP.) and daggers. She wakes up unequipped, has a look around and finds a dead cultist with those items that she can loot and use.

I think that could work, the cultists are insiders, so could have been trusted to carry weapons etc...

Shadowheart could find a sister-cleric who somehow kept their armour and put up a fight before dying, likewise Lazy could loot a killed Githyanki.