It seems like the search being started within hours of him actually starting the hike, would lead to the best results.
Though the search started soon, my bet is that such searches start small unless there are obvious indications that the hiker is in grave danger. For example, the initial search could well of consisted of a ranger driving to the trail head (takes time), then walking the trail.
Once that search yielded nothing, several rangers were probably brought in to drive the paved roads in case he was waiting there, and spot check other probable areas. The area is huge and the rangers would need to decide whether it is better to stay mobile along the roads, or conduct foot searches in smaller areas. In short, the large scale search may of started two days later.
Like, how far could he have gone in that short amount of time? If he became unable to walk there would be a pretty narrow radius to search in.
I go hiking with my children and their friends. The youths are all athletic (running sports) and accustomed to high heat. The bad news is that they all have the physical ability to cover a lot of ground should they get lost (God forbid).
As a very rough guess, I am thinking….
A fit / acclimatized, but not an expert hiker walking with a purpose, but not speed walking can cover at most two miles every hour in flat terrain. Most lost people end up walking with a purpose. Rough, but not mountaneous terrain would reduce this to say 1.5 miles.
This pace could be kept for 3-4 hours before slowing or needing a relatively long break. The pace could then be resumed for another 3-4 hours. Any following pace would be lower.
But… the difficulty for searchers is that the area in the obtainable through the pace in
square miles. Thus a possible 6 mile pace distance is 36 square miles to search. This means a lot of area.