This isn't true, it was a major accomplishment but by far the easiest part of Perelman's papers and not actually even part of the proof of the Poincaré conjecture.
Happy to be corrected on this; I wasn't an active mathematician at the time, so everything I know comes from other accounts.
Moreover I'd strongly dispute that there was any particular point where it was clear that the problem was "near a solution." The W functional is an example where experts could very quickly verify that Perelman had made at least one major new discovery about the Ricci flow. But the proof of the Poincaré conjecture was on another order of complexity and required different (more complicated) new results about Ricci flow.