Posit theories on how the early Equalists were formed, &/or seized power from rivial groups, such as the Triads.
I think there's enough subtle evidence in the series to demystify this subject somewhat. For one, Amon probably learned chi-blocking, directly or indirectly, from one of the Kyoshi Warriors that Ty Lee trained. But whom did he teach this to?
The group that Amon later turned into the first Equalists were likely a gang consisting of non-benders. They were formed in the Dragon Flats Borough, in response to the Triads. Though they hated benders, they were motivated more by greed and prejudice, than by aspirations for equality. This seems oddly specific, but tension between minority groups is often a component in gang warfare, so it's odd that we don't see any criminal gangs of non-benders, besides the Equalists. Unless they were absorbed into the group later on. But Amon didn't win the city through racketeering.
Because of their position in society, the law-abiding non-benders likely did most manual labor and unwanted jobs. Winning these people gives the Equalists knowledge of the city's infrastructure, which explains things like how they can hijack radios. Republic City Underground is clearly not a sewer, so I would guess that they are maintanence tunnels.
These tunnels would have given the Equalists a huge advantage over the Triads. Even if they tried to retaliate after Zolt had his Bending taken away, there's no obvious stronghold to attack. Meanwhile, the Equalists can emerge seemingly out of the city streets.
Of course, I still haven't accounted for a lot of holes, such as "Who was the Lieutenant?" or "How did Amon enlist the aid of Hiroshi?" Partly because there is so little information about these that I would just be wild mass guessing. But, as obvious as the above theory seems to be to me now, I only came up with it relatively recently, so perhaps there are other things that I've overlooked.