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People have said in the past that one of the reasons that the G-man can't be Gordon is that the G-man can talk while Gordon can't.
However...
The original theory says that the G-man is Gordon from a future where technology has advanced significantly enough to allow time travel. It stands to reason that they will also be able to teach a mute to speak.
Also, the G-man speaks as if "unused to human speech".
A clue?
They could probably fix his eyes, too, making glasses redundant, and eye surgery might have changed the eyes from green to blue.