Is the birth of Stack Exchange documented somewhere? How did the system trust users in the very beginning before there were any users with any reputation?
In the earliest earliest days of Stack Overflow, there was no rep requirement for voting, and reduced reputation requirements were later adopted for newer Stack Exchange sites:
Private Public Beta Beta Graduated 1 15 15 Vote Up 15 15 15 Flag Offensive 1 50 50 Leave Comments 1 100 100 Edit Wiki Posts 1 125 125 Vote Down 1 150 150 Create New Tags 1 200 200 Retag Questions 500 750 2000 Edit Posts 1 500 3000 Vote to Close 2000 2000 10000 Access Mod Tools
Remember that the most basic functions (asking and answering) require no reputation at all, so you can build up reputation simply by asking and answering questions and reputation is awarded to you through the community vote.
The reduced reputation requirements allow the early adopters to vote and to start taking control of the community sooner rather than later. Users who have experience on other SE sites also get a 100-rep bonus to get them started. But until the higher-rep users kick in, the Stack Exchange Community Team runs the higher-rep moderator functions.
But going back to the beginning of it all—
The closest thing we have to something documenting the process are the original Stack Overflow podcasts:
The first site, Stack Overflow, started with a private beta. Essentially, founders Jeff and Joel developed and launched this experiment in full view of an enthusiastic and interactive community. The earliest days were a bit of a wild-west endeavor where behaviors and ideas were tested and coded into the system publicly from day one.
So, I guess you can say the earliest Stack Exchange was "bootstrapped" by trusting the community through a process of openness and experimentation until they "got it right"… and the whole thing snowballed to what you see today.