Augustus
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As you can see at Aisha - Wikipedia
it is not really disputed that one of Muhammad's wives was well underage. At least, neither Shia nor Sunni dispute it.
To doubt it would essentially mean to believe that early companions of Muhammad decided to slander him while he was still alive. That, of course, sounds almost completely unbelievable.
It wouldn't be slander though, as there was nothing abnormal about it at the time. It's only in the past century that people have seen it as controversial.
Seeing as she was to become a very controversial figure in the Sunni/Shia rivalry, and there was an episode where Muhammad had to deal with rumours of her infidelity, it is possible that her age was lowered to prove her chastity at the time of marriage and prolong her time spent in the company of Muhammad and thus improve her status
It is also worth considering that the same sources you are trusting for this information are the same sources that had him splitting the moon in 2 and flying around on a winged donkey. Both of these are considered to be hadith of the highest possible level of authenticity, which is always worth bearing in mind when judging everything else.
Hadith and sirah are theology not history, and much of it was invented by medieval jurists centuries later to justify rulings and explain parts of the Quran that they didn't understand.