For that you simply need to have the sudden inspiration of how the scheme works. Snark aside, I don't think that discarding half of the source material as random junk is such an obvious thing to do.
You could easily think, 'hey perhaps the outside triangles are different from the inside ones, lets make a histogram of the symbols in both.'
From there, you'd certainly notice if one side had a lot more symbols than the other side.
Trying to analyze both separately is a decent next step, and we are well along to solving this.
That's not something a normal human would easily think. I doubt an experienced God breaker would have, easily thought your suggestion.
But don't worry, go on telling yourself it's something you would have easily thought.
From there, you'd certainly notice if one side had a lot more symbols than the other side. Trying to analyze both separately is a decent next step, and we are well along to solving this.