How do we know that it's not just that the AI dominates the later stages where the number of permutations has reduced to the point where AI can calculate optima

How do we know that it's not just that the AI dominates the later stages where the number of permutations has reduced to the point where AI can calculate optimal moves? In other words, how do we know that the computer has an edge on the early stages and isn't just breaking even until the later stages with less permutations arrive, at which point it dominates because there are still too many for humans to assess?