200 eager volunteers at a construction site doing whatever they're told by tradesmen managers will raise a structure in remarkable time.
Amish communities also have a history of performing quick builds with volunteer labor from membership.
There has been a substantial population of Amish in northeastern USA within close proximity of WT facilities in New York, New Jersey and Pennsylvania, so it is a real possibility that ambitious WT eyes borrowed the quick build method after observing Amish barn raisings... then of course portrayed the quick build idea as further proof WT is the one true religion with the exclusive blessing of god almighty upon WT construction projects.
WT did not invent the quick build method, and even if it had such would not prove true religion.